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- 16 January – Bellona arrives with Australia's first free settlers
- 22 January – The French d'Entrecasteaux expedition returns to Recherche Bay, Tasmania to rewater and rest.
- 12 February – John Macarthur is granted 100 acres (0.40 km2) of land at Parramatta.
- 16 February – John Macarthur is appointed by Grose as inspector of public works.
- 18 February – A school opens in an unfinished church building is Sydney; the first school had been established in 1789, Isabella Rosson was the first teacher.
- 28 February – d'Entrecasteaux expedition leaves Tasmania towards the Friendly Islands, continuing search for La Pérouse.
- 2 May – Mary Bryant is pardoned in England.
- 15 September – Captain William Paterson leads a party of Scotsmen in the first attempt to cross the Blue Mountains. He is unsuccessful.
- 25 September – Sydney's first church opens.