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- 14 January – Qantas Airways introduces a round-the-world air service from Australia to London.
- 20 January – The Royal Australian Naval College is moved back to Jervis Bay Territory from Flinders Naval Depot in Victoria.
- 28 January to 11 February – Harold Macmillan visits Australia, the first Prime Minister of the United Kingdom to do so while in office.
- 14 February to 7 March – Queen Elizabeth The Queen Mother visits Australia for the second time.
- 21 March – John McEwen replaces Arthur Fadden as federal leader of the Country Party.
- 24 March – The Cahill Expressway in Sydney opens, the first true freeway in Australia.
- 3 April – A cyclone destroys most of the town of Bowen in Queensland.
- 15 April – Monash University is founded in Melbourne, Victoria.
- 11 May – Construction of Australia's largest man-made lake, Lake Eucumbene on the Eucumbene River in the Snowy Mountains, is completed.
- 31 May – Henry Bolte's Liberal government is re-elected in Victoria.
- 19 July – The last tram service runs in Perth.
- 26 August – Robert Cosgrove retires as Premier of Tasmania, and is replaced by Eric Reece.
- 30 September – The ANZAC Day Act 1958 receives Royal Assent, making ANZAC Day (25 April) a national public holiday in Australia.
- 26 October – The wreckage of the Australian National Airways Avro 10 aircraft, VH-UMF Southern Cloud, is found. The aircraft had been missing since 1931
- 22 November – A federal election is held. The Liberal-Country coalition led by Robert Menzies defeats H. V. Evatt's Australian Labor Party with 74 seats to 45 in the House of Representatives, a majority unprecedented since Federation, gained from preferences from the Democratic Labor Party.
- Johnny O'Keefe has his first hit with Wild One
- Radio station 2UE publishes the first Australian Top 40
Science and technology
- Australian engineer Dr. David Warren of Melbourne's Aeronautical Research Laboratories constructs the world's first flight recorder ("black box").
Arts and literature
- 6 February – Simon Baker, race walker
- 20 March – Phil Anderson, cyclist
- 12 April – Glenn Patching, swimmer
- 5 May – Robert DiPierdomenico, footballer and media personality
- 7 May – Alan John, composer
- 11 May – Peter Antonie, rower
- 11 May – Phil Smyth, basketball player
- 3 July – Gary Buckenara, Australian Rules footballer
- 6 July – Gary Humphries, politician
- 13 July – Richard Glover, journalist, author and radio personality
- 15 July –Phil Gould, rugby league identity
- October - Garry Pankhurst, former child actor
- 13 October – Jim Krakouer, Australian Rules footballer
- 6 November – Rocco Ferrentino (born 1958), Australian Entrepreneur
- 31 December – Geoff Marsh, cricketer