I'm not researching the Burchells, but found the obituary at TROVE Digitised Newspapers.
Search at http://trove.nla.gov.au/ndp/del/home
'Family Search' has a baptism record for a Thomas Perry Burchell which could be a possibility (?)
name: Thomas Perry Burchell
baptism/christening date: 21 Sep 1828
baptism/christening place: SAINT MARY,SWANSEA,GLAMORGAN,WALES
birth date: 01 Sep 1828
father's name: Richard Burchell
mother's name: Mary Ann
indexing project (batch) number: C02218-2
system origin: Wales-ODM
source film number: 104493, 104494, 104495, 104496, 104497
Thomas and Sarah's (Victoria, Australia)1856 marriage certificate should contain their parents' names and birthplaces.
Given Names: Thomas Perry
Spouse Surname/Father: ALLEN
Spouse Gvn Names/Mother: Sarah
Reg Number: 2291
I haven't had any luck as yet locating a death record for Thomas Snr.