Governor of New South Wales – John Hunter
Lieutenant-Governor of Norfolk Island – Philip Gidley King
Inspector of Public Works – John Macarthur/Richard Atkins
16 January – Australia's first theatre opens in Sydney. Edward Young's The Revenge and the comedy The Hotel are the first works performed.
23 January – The distillation of spirits is prohibited.
5 February – Soldiers from the New South Wales Corps wreck a house belonging to millwright John Baughan.
10 February – Magistrate William Balmain challenges Macarthur over the house-wrecking incident.
29 February – Macarthur resigns as Inspector of the Public Works and is replaced by Richard Atkins.
June – George Bass makes an unsuccessful attempt to cross the Blue Mountains. Coal is discovered near Port Stephens.
14 September – Governor Hunter complains to the Colonial Secretary of Macarthur’s behaviour.
15 September – Macarthur complains to Colonial Secretary of Hunter’s governing.
9 November – As Sydney grows, Hunter disbands the convict night watch. He divides Sydney into four districts responsible for their own watchmen and orders houses to be numbered.
First beer is brewed in Australia by John Boston.
20 March – Edward Gibbon Wakefield
Henry Vincent, first superintendent of Rottnest Island Aboriginal Prison (d. 1869)
1796 in Australia Wikipedia
Other events of 1796
Timeline of Australian history