Hi Clancy,
I have checked:
1. The National Archives site to see if there is a record for his immigration - no suitable matches.
2. The Ryerson index for newspaper death/funeral notices - no suitable matches (I think that the Vincent Stephen that Sue found could be the one born 1918 in Marickville, whose service record appears on the naa site).
3. The NSW deaths index 1950-1975 - there was an Edward Vincent CLANCY in 1968
4. (Qld indexes only got up to 1964 at present), so I checked The Brisbane city council graves locator - no suitable matches.
5. The Victorian deaths index 1950-1985
http://online.justice.vic.gov.au/servlet/IdxSearch?action=getHistIdxSearchCriteria - 3 matches (I didn't look because you have to pay, and I'm pretty sure that these are available as fiche that I can search for free tomorrow)
NSW has been ruled out as the state. I would guess that if Tas were the state, your family would have said that he emigrated to Tasmania, not Australia, (of course this is just an assumption). Going with the numbers of immigrants, I would say that Victoria, followed by Queensland, Western Australia, South Australia and finally the Northern Territory (which at that time was administered by South Australia) were the most popular destinations, and therefore the order in which to search.
I'll let you know what I can find tomorrow.
Sandra