I'm relieved that someone else has encountered this problem.
The Australia Death Index 'About' information page suggests it is supposed to be complete. The index is not included in the list of World Archive Project that are in progress.
I used the 'Get Help' function to ask whether there is a whole body of data yet to be indexed. As an example, I pointed out that no deaths were recorded in Victoria from 1940 to 1960 for common surnames such as Lawson, Lewis, Martin, Mitchell, Miller and McDonald. In response I received a generic email with links to "helpful articles that explain how you can search for your ancestors using alternate spelling" and how to report transcription errors.
It appears that a big chunk of data has been overlooked. Like me, you will probably have to use alternative research methods such as Trove or Cemetery Records.
It would be great if anyone else could shed some light as this is a very frustrating issue.