Hmm, unfortunately there are lots of people with those names. I think it less likely that they died in NSW if they were ticketed to Melbourne - however

(Each State keeps their own BMDs)
Electoral rolls - each of these has a Thomas Pearson and an Elizabeth Pearson at the same address. The rolls do not show relationships so they could be siblings or parent and child etc. occupations of the women are all home duties, I have included the occupation of the men
1931 at 70 Pearson St, West Brunswick, Victoria. Occupation; machinist
1936 at 171 Union St, Newtown NSW - he is a labourer, she a machinist
etc etc
This death looks a possible - is this his mother's name?
1970,
Thomas MCKENZIE
parents: John, Mary MUNRO
aged 85.
Place of death HUGH
Registered Victoria #11527.
I see a cremation which appears to match this:
http://www.deceasedsearch.com/index.phpAt SPRINGVALE BOTANICAL CEMETERY
THOMAS MCKENZIE
Religion NONE
Date of Service 29/05/1970
Location Details BANKSIA, WALL NICHE SINGLE, WALL BJ NICHE 03
Sommeone may be able to do a newspaper look up to see if there is a death notice.
I could not find an appropriate death that matched Elizabeth.
Judith