An old artist (Rolf Harris) sets up some paintings at Luna Park, Sydney, planning to sell them, but has trouble attracting any people until he performs "Jake the Peg". Most of the crowd move on again when the performance finishes, being uninterested in his paintings, so he starts telling his granddaughter about their origins.
We then travel back in time to a British convict ship, the "Northern Star", as it sails towards a tiny colony on Sydney Cove with sixty-four convicts on board. Six of these convicts are a young boy named Toby Nelson, his older sister Polly, "Big George" Tomkins, a blacksmith, Jake "Dipper" Davey, a professional pickpocket who had only been nabbed when he became old and slow, William Watts, a "village idiot" who was on board for stealing a pig from a farmer - he had been caught when he tried to sell the same pig to the same farmer on the same day, an action that led to him being nicknamed "Silly Billy" after his trial - and Jack Doolan, a highwayman who had used some money he had robbed to buy bread and cheese, which he was passing around to a group of hungry people when the constabulary found him. Jack had given Toby the reins of his horse and Polly some of the bread and cheese, which led to them being charged as two of "the Doolan gang".
After a journey of eight months, the Northern Star sails through the headlands into the harbour on whose shores the colony is built. The convicts are greeted by the Lieutenant Governor, Colonel Lindsay Lightfoot, left in charge of the colony while the Governor is inspecting Norfolk Island. He reads out the rules of the colony and warns the convicts of the consequences of disobedience of orders. Toby and Polly see each other for the first time since the ship left England - women convicts had been kept in a separate area - but their reunion is cut short by a tall officer, Sergeant "Bully" Langden.
Bully tells Colonel Lightfoot's aide, Captain Pertwee, that the military need five men to work on the Government farm, and he selects Big George, Jack, Dipper, Silly Billy and Toby for the task. Polly is taken away from the docks by Colonel Lightfoot's wife Augusta to assist her cook and laundrymaid. Toby falls to the ground before the convicts can be given the order to march. When Bully kicks away a cup of water that a woman tries to give Toby, Big George confronts Bully, who has to be rescued by several other soldiers. He decides to fix the troublemaking by marching the convicts straight to the blacksmith's shop, where they are each fitted with heavy chains around their ankles.
Early next morning, the five convicts are aroused by Bully's deputy, Corporal "Weazel" Wesley, who issues them with a small ration of bread and some work tools before marching them out to begin their first day's work. Toby starts to struggle when the day gets hotter, but Dipper is the first to fall, gasping with pain and holding his bad leg trying not to collapse. The other convicts carry him to the shade, give him some water and fan him with his hat. He starts to recover when Weazel finds them. Jack cheerfully invites Weazel to join their "picnic", but Weazel aims his rifle at Jack's heart. A shot is fired, but Bully, who had fired the shot at a group of kangaroos in the scrub, calls on Weazel to help him. They soon find another slower target in the form of a koala and shoot it dead. Toby tries to rescue the baby koala who is on his dead mother's back, but he is caught by Bully, who throws the baby koala back into the bush.
That night, Toby is too unhappy to either eat dinner or talk to anyone. As his friends lay down in their rough bunks, Dipper brings out a small round object, and as he opens it up, it begins to play some music. The object is a gentleman's watch with a music box in it, the only possession Dipper can truly call his own - it was given to him by his father, and long ago had been worn by Dipper's great-grandfather. The music sends Dipper's friends to sleep, allowing him to creep out of the hut and distract the guards by throwing some pebbles. As they chase after what they suppose is an intruder, Dipper sneaks back to the work site, finds the baby koala back near his mother's body, tucks him in an inside pocket that the baby thinks is his mother's pouch, and returns to the hut, distracting the guards again with some wild animal noises. In the hut, he takes out the baby koala and puts it in the crook of Toby's elbow. Toby wakes up and sees the koala and his face turns to joy, but no one, least of all Dipper, will admit to knowing how it got there.
Four weeks on, Polly has become Augusta's only servant girl, and spends time shopping at the store so she can hear the news of the convicts. She finds out that Bully was reprimanded by the Lieutenant Governor for leaving the prisoners while he was shooting at the kangaroos. After Polly hears that Toby is allowed to keep his pet koala and Bully is ordered to remove Toby's leg-irons, Augusta sees Polly smile for the first time.
At tea that night, Polly hears from Captain Pertwee that one of the convicts has been injured and, according to the surgeon, may not live. Terrified, she runs up the streets of Sydney Town towards the convicts' hut, but finds out that it is not Toby who is dying, but Dipper. The convicts had been felling trees, and Dipper had suffered another one of his leg cramps, but was ordered to continue working by Bully. Unable to move, Dipper couldn't get out of the way of a large and heavy trunk when it crashed to the ground so quickly that the other convicts weren't able to help him. With his last bit of strength, Dipper presses something into Toby's hand and tells him that he wants him to have it. When the other convicts have moved away, Toby shows the object, the music box watch, to Polly.
In the days that follow Dipper's burial, Jack's behaviour changes: he stops making cheeky remarks to Bully as they work, he no longer calls Corporal Wesley "Weazel" to his face and is allowed to hold the reins of Bully's mare as he quietens and calms it each morning. Toby often sees Jack looking towards the distant Blue Mountains, and one night hears Jack and George whispering to each other, and knows that Jack is planning to escape, not wanting to suffer the same fate as Dipper. All seems normal at the work site the next morning, until George starts breaking all of the tools in pieces, drawing the attention of the soldiers and allowing Jack to untether the friendly horse and quietly turn it towards the mountains.
Later that day, George is made to pay for assisting in Jack's escape: he is given fifty lashes while tied to a large wooden triangle in the public square and thrown into a punishment cell on Bully's orders where he will spend every night for the next six months while he works at the blacksmith's shop during the day. Weeks later, Toby mouths the word tonight to George as he and Billy pass the cell on their way to work. That night, Polly—whom the Lightfoots have given permission to visit George in the punishment cell—and Toby smuggle some food from the Governor's kitchen and see George in the cell. George longs for Jack to help him escape the cell and Toby comes up with a plan to search for Jack in the bush, taking the bundle of food intended for George and his own pet koala. A noise causes Bully and Weazel to wake in the guardhouse and see Toby's shadow between the wire fence and scrub. Toby runs for his life and doesn't stop until he cannot hear the shouts of the pursuing guards behind him.
As he continues to search for Jack in the night while keeping a tall mountain peak in front of him to stop him going around in circles he gets a feeling that someone is following him, but he hears little and doesn't see anything when he stops to look. He is sure that if it is one of the guards, they would make much more noise. He eventually flops onto the ground exhausted and sleeps until the early dawn when he is woken by a kookaburra and some cockatoos. He eats some of the provisions and then resumes his search.
That evening, with his throat sore from calling Jack's name and all of the food Polly had provided gone, he is close to exhaustion when he finds a clearing with the remains of a dug-out fire. He feels the fire's ashes to see how warm they are when the sound of a snapping twig causes him to turn around. He sees a young Aborigine with a spear in his hand and a dingo at his side. But although Toby is terrified at first, he soon realises that the other boy is actually a friend. They get to know each other with their arms and some sand providing them with ways to overcome their natural language barrier. Toby eventually finds out that his new friend is named Wahroonga and he had been following Toby through the bush to make sure that no harm came to him or his koala. Wahroonga introduces Toby to his animal friends—a dingo and a cockatoo—and shows him how to find water and food and invites him to stay the night in a gunya, an Aboriginal sleeping shelter on the edge of the clearing.
Next morning, after Toby explains that he is trying to find Jack—a man riding on a horse—Wahroonga leads him along a dry river bed until they find a horse's hoof prints. They spend the next few hours following the river bed looking for more prints and other small clues to Jack's possible escape route. At one point, Wahroonga motions to Toby to stand still as he hears a horse neighing and they hide behind a bush as two bushrangers pass them. Just as Toby and Wahroonga are ready to leave their hiding place, they hear a third horse approach them. They try to bury themselves in the sandy creek bed, but Toby hears the horse slow and stop. Then footsteps approach them and a foot taps Toby on the shoulder. He is scared when he first turns around, until he realises that it's Jack Doolan.
After introducing Jack to Wahroonga, Toby tells him stories of his adventures in the bush, but when Jack thinks Toby has run away too, he tells him about what has happened to Big George and why he ran away. Jack follows the path the bushrangers took earlier and above their camp, he gets Toby and Wahroonga to roll a large boulder down the hill into the camp. It smashes into one of the huts, giving Jack a chance to unleash both of the horses and send one into the bush while he gallops back to the boys on the other. Moments later, Jack is back on his horse with Toby, Wahroonga and the koala on the other, with the dingo following them and the cockatoo overhead as they make their way back towards Sydney Town.
On the edge of the convict settlement, Jack tells Toby that they will need to distract the guards to allow them to get near George's cell, and they will need some tools to break down the cell door. Toby remembers seeing tools in the storehouse next to the cell. As the guards are being served tea and stew, Jack gives a signal and Wahroonga gives a soft whistle to the cockatoo, which flies toward the line of soldiers and causes them to scatter in all directions. Another signal from Jack causes Wahroonga to whisper a command to the dingo which snaps and snarls at the soldiers' horses causing them to rear and plunge, break their tethers and bolt toward the bush. The soldiers set off in pursuit and leave the settlement unguarded. Wahroonga keeps watch as Jack and Toby head for the storehouse. They find no tools there, only barrels of rum and oil. Jack gets Toby to open the oil barrels while he takes the rum and pours some into the soldiers' tea mugs and the rest into the boiler of tea. He makes it back to the store house just as the soldiers return with their horses.
The soldiers drink the tea and line up for several cupfuls from the cook, who eventually tastes the brew for himself, all getting drunk on the rum Jack had put into it. As they boisterously continue drinking the tea, Jack sends Toby to collect Silly Billy while he heads for the guardhouse to get the keys to Big George's cell. With all three convicts back in the storehouse, Jack begins to pour some of the oil on the ground while Toby and Billy take the key and unlock the punishment cell. Silly Billy yells at George in case he is asleep, but Bully hears the noise and tries to rouse the soldiers. Jack hurls the last barrel of oil to the ground and hops over it before it spreads everywhere. The convicts think they will be trapped by the soldiers, but one by one the soldiers slide on the oil and fall to the ground. Despite his drunken state, Bully stays focused on Jack and while kneeling, he aims a rifle at him. At that moment, a boomerang thrown by Wahroonga hits Bully on the back of his neck, sending his gunshot through a window of the Governor's house (causing a frightened Polly to drop the oil lamp she is carrying) before he falls unconscious to the ground.
At the first shouts of the commotion made by the drunken soldiers, Colonel Lightfoot, convinced by his wife Augusta that the Aborigines were attacking the settlement, had dashed out of the house with a sword in his hand leaving her on her own. She hears light footsteps and sees a flickering gleam of lights, and when the door opens, she faints out of fear before she can find out what happened. Polly is also trembling with fright - the lights come from the flame of the dropped lamp which ignited on the now-spreading oil. The fire engulfs the house so fast that Polly and Augusta are trapped inside.
As the four convicts begin their escape, Wahroonga sees the flames coming out of the house and signals to them. Big George recognises it as the Governor's house, and leads a mad dash toward the building. There is smoke and flame coming out of every window as they arrive, and they can hear Polly's and Augusta's cries from within. George finds a large water barrel with a bucket beside it, throws some water over himself and Jack and gets Toby to throw more water on them as they smash the door off its hinges. Inside, George follows the sound of Polly's cries and sees her and Augusta at the bottom of a staircase, with a fallen beam blocking their escape.
George bends over and puts his shoulders underneath the large beam, straining his body to slowly ease it up enough for Augusta and Polly to leave. Hearing a squad of soldiers led by the Lieutenant Governor himself, Toby contemplates escaping, but throws more buckets of water on Billy, Jack and himself before they rush in to guide Polly and Augusta out of the house. With all five of them outside, George heaves the beam off his shoulders and rushes to join them as the house begins to collapse behind him. Polly and Augusta fall into the arms of their respective brother and husband. A couple of hours later, the four convicts explain to Colonel Lightfoot all of the things they did, why they did them and who had helped them. Toby tries to introduce Wahroonga in the middle of his story, only to discover that he has disappeared into the shadows of the bush along with his dingo and cockatoo, which gives a farewell shriek on its way towards the mountains.
The artist wraps up his story by telling us that Bully is found guilty of being drunk on duty and locked away in the same punishment cell into which he had thrown Big George, until his temper improved, while the Lieutenant Governor grants the brave convicts who saved his wife full pardons and grants of land on which they could start their own farms - a happy ending for Billy, George, Jack and Polly. He starts to tell us about Toby, but then looks at his watch and realises that he has to end the story because it's getting late. He tells us that the watch plays a little tune when he opens it up, and he has had it for several years, ever since it was given to him by a dear old man named Dipper. He then points his granddaughter to the nearby merry-go-round, where the people that she sees on it bear likenesses to the characters from his paintings and the animation.
The movie was a commercial disappointment. "It was screening in the mornings only, which is bloody nonsense," said Gross. "We realised that we'd always be struggling for screens because those big companies were committed to American movies. We were playing against 'The Muppets', so why would they invest any money to promote our films? That's when we began to move more and more into television."