Incumbents

• Monarch Elizabeth II
• Governor-General Sir William Slim
• Prime Minister Robert Menzies

State premiers

• Premier of New South Wales Joseph Cahill
• Premier of Queensland Frank Nicklin
• Premier of South Australia Thomas Playford IV
• Premier of Tasmania Robert Cosgrove (until 26 August), then Eric Reece
• Premier of Victoria Henry Bolte
• Premier of Western Australia Albert Hawke

State governors

• Governor of New South Wales Sir Eric Woodward
• Governor of Queensland Sir Henry Abel Smith (from 18 March)
• Governor of South Australia Sir Robert George
• Governor of Tasmania Sir Ronald Cross, 1st Baronet (until 4 June)
• Governor of Victoria Sir Dallas Brooks
• Governor of Western Australia Sir Charles Gairdner

Events

• 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.

Unknown dates

• Johnny O'Keefe has his first hit with Wild One
• Radio station 2UE publishes the first Australian Top 40

Science and technology

• 26 January The HIFAR nuclear reactor at Lucas Heights goes critical for the first time.

Unknown dates

• Australian engineer Dr. David Warren of Melbourne's Aeronautical Research Laboratories constructs the world's first flight recorder ("black box").

Arts and literature

• 11 December The National Institute of Dramatic Art (NIDA) opens in Sydney.
• William Edwin Pidgeon wins the Archibald Prize with his portrait of journalist Ray Walker
• Eric Smith wins the Blake Prize for Religious Art with his work The Moment Christ Died
• Randolph Stow wins the Miles Franklin Award for To the Islands
• Russel Ward releases The Australian Legend

Film

Television

• 1 November The first episode of Bandstand goes to air on TCN-9, hosted by Brian Henderson.
• 22 November The Australian federal election, 1958 is the first to be televised.

Sport

• Athletics
  • 23 March John Russell wins his second men's national marathon title, clocking 2:40:30 in Sydney
  • 6 August Herb Elliott sets a world record for the one-mile dash (3:54.5) at Morton Stadium in Dublin, Ireland.

• Cricket
  • New South Wales wins the Sheffield Shield

• Football
  • Brisbane Rugby League premiership: Brothers defeated Valleys 22-7
  • New South Wales Rugby League premiership: St. George defeated Western Suburbs 20-9
  • South Australian National Football League premiership: won by Port Adelaide
  • Victorian Football League premiership: Collingwood defeated Melbourne 82-64

• Golf
  • Australian Open: won by Gary Player

• Horse Racing
  • Sir Blink wins the Caulfield Cup
  • Yeman wins the Cox Plate
  • Skyline wins the Golden Slipper
  • Baystone wins the Melbourne Cup

• Motor Racing
  • The Australian Grand Prix was held at Bathurst and won by Lex Davison driving a Ferrari

• Tennis
  • Australian Open men's singles: Ashley Cooper defeats Malcolm Anderson 7-5 6-3 6-4
  • Australian Open women's singles: Angela Mortimer defeats Lorraine Coghlan 6-3 6-4
  • Davis Cup: Australia is defeated by the United States 3-2 in the 1958 Davis Cup final

• Yachting
  • Solo takes line honours and Siandra wins on handicap in the Sydney to Hobart Yacht Race

Births

• 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
• 13 October Jim Krakouer, Australian Rules footballer
• 6 November Rocco Ferrentino (born 1958), Australian Entrepreneur
• 31 December Geoff Marsh, cricketer

Deaths

• 8 April Ethel Turner (born 1872), writer
• 13 September Russell Mockridge (born 1928), cyclist
• 14 October Douglas Mawson (born 1882), polar explorer
• 30 November Hubert Wilkins (born 1888), polar explorer