Towards the end of 1802, Woodriff was appointed to command of the , a 50-gun ship armed "en flûte", and fitted to transport convicts. They were bound for Port Phillip in the Bass Strait, on the southern extremity of Australia, with the intention of setting up a settlement there under the command of David Collins. "Calcutta" sailed from Spithead on 28 April 1803, in company with the storeship "Ocean", calling at Rio de Janeiro in July, and the Cape of Good Hope in August, arriving at their intended destination in October. "Calcutta" then sailed alone to Port Jackson to take on a cargo of of timber. Whilst in Sydney, Woodriff and the crew of "Calcutta" assisted in suppressing the Castle Hill convict rebellion. For that service, Woodriff received a land grant near Penrith, New South Wales in 1804.