Have you tried the national archives -
www.naa.gov.au A search gives 112 hits for William Dowling. A brief look gives (as an example)
DOWLING ROWETT STANLEY : Service Number - V34296 : Date of birth - 28 Mar 1920 : Place of birth - CARNEGIE VIC : Place of enlistment - ARMADALE VIC : Next of Kin - DOWLING WILLIAM
This COULD (only could) be a son of your William. There are probably others that may give some ideas.
The records from NAA can be seen for no charge, by requesting they be digitised & put online.
The main records you will get are WW1, WWII and immigration post 1945.
Trish