1837 in Australia
- 2 January - The Supreme Court of South Australia is established by Letters Patent, five days after the founding of the colony.
- 6 March - The Theatre Royal in Hobart opened. It remains Australia's oldest working theatre.
- 28 March - The Hoddle Grid of streets for the central business district is surveyed by Robert Hoddle.
- 1 June - First inner-city land sale in Melbourne.
- 10 June - The first whale is caught in Western Australia.
- 10 February – Frederick Goulburn, first Colonial Secretary of New South Wales (b. 1788)
- William Cox
- Joseph Gellibrand
- Francis Greenway
- James Ruse