The earliest mention I have found of the song in Australian newspapers appeared in an advertisement for a concert in Sydney in 1851

The Sydney Morning Herald Monday 15 September 1851 p. 1.

see http://nla.gov.au/nla.news-article12930347

part of which reads

....
Gum-tree Canoe............. Mr. Nash
….
Admission 2s.
Tickets to be obtained at the Royal Hotel ;
Masonic Hall, York - street ; Music Store,
of Mr. Henry Marsh, 490½, George - street ;
and at the door on the evening of performance.
Doors open at a quarter-post 7 ; commence
at 8 o'clock.