Looking at Thomas Coopers born after 1880, unless he is older of course, in Tasmania finds six possibilities, also taking note of the parents. Then, looking at deaths of Thomas Coopers in Victorian BDM index for these same parent possibilities shows one instance of repeat parents ie parents for birth in Tas/parents at death in Victoria-
Thomas Samuel Cooper d. Malvern 1975 age 82yrs parents Joseph Cooper and Margaret Yost.
Tas BDM - Joseph Cooper m. Margaret Yost 8 Jul 1885 21/26yrs Portland #901(Thomas is b. 1892)
Also in Tasmania - Christina Yost m. Thomas Holland 11 Oct 1894 23/24yrs Portland #700and you would have to think that these women are sisters
Victoria BDM - Hilda Mary Holland m. Leonard Alfred Cooper 1937 #15501 Death of Hilda Mary Cooper 1971 NORT 63yrs #25033 parents Thomas Holland and Christina Yost.
If this Thomas Cooper death is not among the ones you have obtained, I think it would be worth risking another try for his death record - and you could cancel the Tas. purchase.
And if you have seen this death certificate and it is not your Thomas, then forget the above.