The following lists events that happened during 1798 in Australia.

• Monarch - George III
• Governor of New South Wales – John Hunter
• Lieutenant-Governor of Norfolk Island – Philip Gidley King
• Inspector of Public Works – Richard Atkins

• 2 January – George Bass sights Wilsons Promontory
• 26 January – The koala and lyrebird observed by John Price on an expedition led by John Wilson
• 12 February – Matthew Flinders explores the Furneaux Islands
• 25 February – John Hunter names Bass Strait in honour of George Bass
• 14 May – HMS Nautilus arrives in Sydney, carrying missionaries from the London Missionary Society
• 1 October – Sydney's first church St Philip's is destroyed by fire
• 7 October – George Bass and Matthew Flinders leave Sydney to explore Van Diemen's Land on the Norfolk
• 7 October – St Phillip's Church founded in Sydney, completed in 1809
• 8 November – Nauru discovered by John Fearn
• 9 December – Bass and Flinders confirm the existence of the Bass Strait
• 22 December – Norfolk enters the Derwent River
• 25 December – George Bass climbs Mount Wellington

• Barker, Anthony (1996). What Happened When. St Leonards: Allen & Unwin. ISBN 978-1-86373-986-3.
• National Library of Australia. "The World Upside Down: Australia 1788 – 1830". Archived from the original on 20 March 2007. Retrieved 9 February 2007.