With the surname cleared up, and the census stating William was born Down Under, here's his birth details to take it back another generation:
William Purcell, b. 25 Sep 1820 at Port Dalrymple, New South Wales, Australia; baptised St. Philip's, Sydney, N.S.W. 27 May 1821.
His parents were John & Ann Purcell. The only other child I can see for this couple in Australia is Elizabeth, baptised the same day and place and William. She was born in Hobart, Van Diemen's Land (now Tasmania), on 22 May 1818.
A John "Pussel", son of John & Ann, was born in Hobart, Tasmania 25 Dec 1822, baptised there 6 Jan 1823 - not sure if this is another of the Purcell children, though the entry does state his parents were married in England.