Have you taken a look at the Ryerson Index? www.ryersonindex.org This is current clippings from newspapers. The privacy rules in Australia generally won't allow you to get death dates from the certificates until 25-30 years have passed. If he died in WWII or any other war you may be able to find his records and death date from the National Archives or, perhaps, the Australian War Memorial. If he died before the mid 1950's then you may find a death date, obituary, etc from the newspapers on Trove.
A google search will sometimes come up with what you're looking for.