Charles WARMAN - Tasmania

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My Great great great grandfather Charles Warman was in Tasmania between 1829 and 1832. He travelled from Kent to Hobart on the Swiftsure in 1829 and then to Sydney on the Harlequin in 1832, where he was joined the following year by his wife Elizabeth (nee Reynolds) and their daughters Elizabeth, Jane and Ann(e).

I am wondering the best way to find out about his time in Tasmania.