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This is a VERY long shot and I can't see how it could be proved that this is the correct person.

New South Wales, Australia, Unassisted Immigrant Passenger Lists
Arrival, Sydney 9 July, 1866
Ship Ellen Southard
The list shown are all crew, with the position held by each person next to their name and among them is:
William Donnelly, 22, OS, Nationality given as Great Britain (OS = Rank of Ordinary Seaman which implies that he had had little or no previous experience as a sailor)
Ship came from Tome which is in Chile, while newspaper reports say it left Talcahuano, Chile which is about 30k  away from Tome, having left Chile on 28 March.  The ship appears to have been carrying wheat and flour.
There are a number of mentions in Trove but all with similar information although one mention suggests that it is an American ship
From the Sydney Mail, Sat 21 Jul 1866
ELLEN SOUTHARD, American ship, 828 tons, Howe, at Walker's Wharf, agents: Wilkinson Brothers, and Co.
Wikipedia says: Ellen Southard plied international trade routes from her homeport in Bath, Maine, with visits documented in ports as far away as Sydney, Australia.
Trove has the Ellen Southard in Sydney in 1865 and she leaves Sydney at about the end of June 1865 bound for New Caledonia. I don't know where she went between bein in New Caledonia and Chile - maybe back to the US?

So perhaps this is William???

Judith