shipstamps.co.uk

I found a web-site http://www.davidbrown1801nsw.info (click on chapter 5) which give that she was an American brig of 158 ton and arrived at Sydney from India in June 1809 with a speculative cargo, not any builder, homeport of dimensions given. Only that the captain was an American Arnold Fiske.
She was bought by an Australian syndicate, but the booklet “Ships of Australia and New Zealand before 1850 by Ronald Parsons gives not any detail of her, so it looks that she was not registered in Australia.
In the web-site is given that she sailed regular between Sydney and Calcutta four times a year.

William Mariner (1791–1853) was an Englishman who lived in the Tonga Islands from 29 November 1806 to (probably) 8 November 1810. He wrote an account of his experiences, Tonga Islands, that is now one of the major sources of information on pre-Christian Tonga.

He began his adventures at the age of 13 aboard Port Au Prince. Tonga issued five stamps on 16 June 1983 on the advantures of William Mariner.

Despite his favored position in Tonga, William Mariner longed to return to his family in England. Captain Fisk of the New South Wales brig Favourite, 130 tons, sailing out of Port Jackson with 90 tons of pearl shells from the Society Islands, and sandalwood from Fiji, agreed to give William passage to Macau in Nov 1810.

Source: Wikipedia