Monarch – Elizabeth IIGovernor-General – Sir William SlimPrime Minister – Robert MenziesPremier of New South Wales – Joseph Cahill (until 22 October), then Robert HeffronPremier of South Australia – Sir Thomas PlayfordPremier of Queensland – Frank NicklinPremier of Tasmania – Eric ReecePremier of Western Australia – Albert Hawke (until 2 April), then David BrandPremier of Victoria – Henry BolteGovernor of New South Wales – Sir Eric WoodwardGovernor of Queensland – Sir Henry Abel SmithGovernor of South Australia – Sir Robert GeorgeGovernor of Tasmania – Thomas Corbett, 2nd Baron Rowallan (from 21 October)Governor of Victoria – Sir Dallas BrooksGovernor of Western Australia – Sir Charles Gairdner26 January (Australia Day) – Darwin was granted city status12 February – The Melbourne outdoor performance venue the Sidney Myer Music Bowl is officially opened by Prime Minister Robert Menzies.15 February – American evangelist Billy Graham begins a tour of Australia.February – major floods in Queensland March – formal construction of the Sydney Opera House began4 June – the Soviet embassy in Canberra was reopened. It had been closed since 29 April 1954 as a result of the Petrov Affair 29 July – Qantas launched its first jet service from Sydney to San Francisco via Nadi and Honolulu.August and September – Princess Alexandra toured Australia September – Australian National University building an "Atom Smasher" 23 September the M/S Princess of Tasmania Australia's first passenger Roll-on/roll-off diesel ferry makes maiden voyage across Bass Strait.November – Donald Bradman batted for 15 minutes in a demonstration. He retired from cricket.Arts and literature
William Dobell wins the Archibald Prize with a portrait of Dr Edward MacMahonThe Big Fellow by Vance Palmer wins the Miles Franklin Literary AwardOn the Beach starring Gregory Peck and Ava Gardner was shot around Melbourne. The film was based on the novel by Nevil Shute.
Six O'Clock Rock screened on the Australian Broadcasting Commission's channel. It was compered by Johnny O'Keefe and was the ABC's response to Bandstand on Channel Nine.
Adelaide's first television station, NWS-9, begins broadcasting on 5 September
CricketNew South Wales wins the Sheffield ShieldEngland toured Australia in the summer of 1958/59 for The Ashes; Australia won the series 4-0.FootballBrisbane Rugby League premiership: Northern Suburbs defeated Brothers 24-18New South Wales Rugby League premiership: St. George defeated Manly-Warringah 20-0South Australian National Football League premiership: won by Port AdelaideVictorian Football League premiership: Melbourne defeated Essendon 115-78GolfAustralian Open: won by Kel NagleHorse RacingRegal Wench wins the Caulfield CupNoholme wins the Cox PlateFine and Dandy wins the Golden SlipperMacdougal wins the Melbourne CupMotor RacingJack Brabham wins the 1959 Formula One Drivers' ChampionshipThe Australian Grand Prix was held at Longford, Tasmania and won by Stan Jones driving a MaseratiTennisAustralian Open men's singles: Alex Olmedo defeats Neale Fraser 6-1 6-2 3–6 6-3Australian Open women's singles: Mary Carter defeats Renee Schuurman 6-2 6-3Davis Cup: Australia defeats the United States 3-2 in the 1959 Davis Cup finalYachtingSolo takes line honours and Cherana wins on handicap in the Sydney to Hobart Yacht Race29 January – Nick Xenophon, lawyer and politician31 January – Anthony LaPaglia, actor8 February – Andrew Hoy, equestrian rider12 February – Sigrid Thornton, actress24 February – Mike Whitney, cricketer5 March – Colleen Noonan, mother25 April - Jennifer Margaret Le Cussan, Botanist5 June – Mark Ella, rugby union player21 July – Paul Vautin, rugby league footballer, coach and media personality26 July – Gary Honey, long jumper29 July – Gene Miles, rugby league footballer of the 1980s and 1990s12 August – Kerry Boustead, rugby league footballer19 August – Rodney Adler, businessman30 August – Mark "Jacko" Jackson, footballer and actor12 September – Brad Dalton, basketball player6 October – Robyn Maher, basketball player11 October – Wayne Gardner, motorcycle and touring car racer24 October – Rowland S. Howard, musician (died 2009)4 September – Kevin Harrington, Australian actor13 November – Anne Manning, racewalker1 December – Wally Lewis, rugby league footballer and coach12 December – Christine Stanton, high jumper15 December – Greg Matthews, cricketer22 February – Harold Hardwick (born 1888), freestyle swimmer20 June – Sir Ian Clunies Ross (born 1899), scientist8 August – Albert Namatjira (born 1902), Aboriginal artist19 September – Arthur Hennessy (born 1876), Australia's first rugby league captain14 October – Errol Flynn (born 1909), actor (died in Canada)14 October – Jack Davey (born 1907), radio comedian and quiz show host22 October – Joseph Cahill (born 1891), Premier of New South Wales (1952–1959)10 November – Gertrude Bodenweiser, choreographer11 November – Charles Chauvel (born 1897), filmmaker24 November – Dally Messenger (born 1883), rugby union and league footballer18 December – Edouard Borovansky (born 1902), Czech born ballet dancer and choreographer; founder of the Borovansky Australian Ballet 