Hi there,
Could there be several families in Tas in 1840's with surname Edsall
Not sure, if this helps find Henry's origins but at Tas Archives Office's online index arrivals and departures for Edsall,
Arriving on Bardaster on 10 Dec 1837, there's Brook, Edward, Eliza, Hellen, Mary and Samuel
Two departures for surname Edsall
On Raven, from Launceston 6 Sept 1849 to Port Phillip (Melbourne) Mrs Edsall ex Bardaster 2 children born in the Colonies, each noted as child of Mrs ; Brook born in the Colonies
On Lady Bird, from Launceston 28 Feb 1854, Mr Edsall, having arrived in Tas on Lady Bird
http://www.archives.tas.gov.au/nameindexes (Tas Archives accepts submitted entries

Cheers, JM