Morris’s first role came at the age of 10 when she was part of the cast of the television episode "Picture of the Magi" a Family Theatre production which aired about 1957 on the Mutual Broadcasting System in the United States. She then performed in two other roles in the USA, at the age of 10 on the Loretta Young Show, and in 1960, at the age of 13, on The Chevy Mystery Show hosted on that occasion by Vincent Price.
Returning to Australia, Morris's next role was not to come until she reached the age of 20 when, in 1967, she worked in the television series, Bellbird. Impressing casting agents, she was cast in numerous well known television series, including (see drop-down filmography list for further details) seven episodes in Division 4, four episodes in Matlock Police and three episodes in the Homicide series.
During this time she also moved to more provocative (for its time) television, especially in the sex series of Alvin Purple, and then under the direction of Tim Burstall as Sybil the babysitter in Libido: The Child (one of four parts of a portmanteau film that showed various aspects of human sexuality). In this part Morris awakens the sexuality of the boy that she is babysitting. For her part, Morris won the 1973 Australian Film Industry (AFI) Best Actress in a Lead Role.
Morris then played the part of "Sam" in the 1978 movie In Search of Anna, before receiving top billing as the wife "Jill Cowper" in the 1979 black comedy The Plumber, which began its life as a small 6 week television series directed by Peter Weir but following its success was produced as a DVD titled The Mad Plumber.
The 1980s brought further success. She starred in Maybe This Time (1980), Strata (1983), Phar Lap (1983) as Bea Davis, the wife of Phar Lap's owner David J. Davis, and played the part of "Catherine Faulkner", the mother of the main character, "Kat Stanton", (played by Nicole Kidman) in Bangkok Hilton (1989). In 1986 Morris was cast as Margaret 'Meg' Stenning in the miniseries The Last Frontier, that also starred Jason Robards as her father Edward Stenning, fellow Australian Jack Thompson as her brother, the black sheep of the family, Nick Stenning, and American actress Linda Evans as Kate Adamson-Hannon. (This miniseries was released on November 3, 1986).
During and after this work she also played the role of "Liz Beare", the daughter in law of "Maggie Beare" (played by Ruth Cracknell) in the Mother and Son series that ran from 1984 to 1994.
Following this, amongst other work, she was cast in the role of "Mrs Muggleton" in eight episodes of the Spellbinder (1995) television series.
Morris wrote and directed the comedy Luigi's Ladies in 1989. Later she teamed up with George Miller and Dick King-Smith to write Babe: Pig in the City in 1998.
An episode of Dinotopia in 2002 and then most recently co-wrote the story to the film Happy Feet (along with Warren Coleman, John Collee, and once again, George Miller). Happy Feet was the first Australian animated film to win the Academy Award for Best Animated Feature, and for her part in writing it Morris was nominated for an Annie Award.
She wrote the screenplay for Fred Schepisi's 2011 film, The Eye of the Storm, based on the novel of the same title.
Morris has been nominated for several awards in her career including:1973 Nominated and won Australian Film Institute (AFI) award for Best Actress in a Lead Role for Libido: The Child.
1977 Nominated by the AFI for the Best Actress in a lead role for her work in The Picture Show Man.
1980 Nominated by the AFI for Best Actress in a lead role for Maybe This Time.
1986 Nominated by the AFI for Best Actress in a lead role for The More Things Change.
2007 Nominated for an Annie Award for the Best writing in an Animated Production for Happy Feet.