I have a book with the names and details of all the passengers on the SS Great Britain between 1852-1875.
There is only one entry with the surname you're researching and that is:
John Caffery, age 21, Irish, Labourer.
He sailed from Liverpool to Melbourne, leaving on 15th Dec 1867. The journey took 57 days and there were 512 passengers on board.
Probably of no help to you but then again, it is the same surname and may be.
