At the website for the Victorian Public Records Office (pro.vic.gov.au/provguide-50), one may see ships' passenger lists for early immigrants. At that site there is an Index to Assisted British Immigration 1839-1871. I did a quick online search and found an entry for Henry DAVIS in 1840, namely, Mr Henry DAVIS, June1840 on the ship 'Andromache' in Book no 2, Page 127.
The Victorian Registry of Births, Deaths and Marriages sells some historical BDM indexes and, one of them, the Digger - Pioneer Index. Victoria 1836-1888, reveals 2 possible registered deaths for Henry MORGAN: one for a Henry MORGAN aged 57 with a birthplace SHRO (possibly, Shropshire, England) who died in 1865 (registration no. 7088) and another for a Henry MORGAN aged 70 with a birthplace SOME (possibly, Somerset, England) who died in 1871 (reg'n no 4703). I don't know when your man was born - if it was early in 1880s, these entires might interest you. If so, death certificates can be purchased by online order at the Registry's website.
Hope this helps.