A possibly stupid question, sorry. I'm making the assumption that your parents were born and married in England or Wales. If so then it should be fairly simple to trace their parents. I'm not that conversant with Australian records, but the few marriage certificates I do possess show both sets of parents.
I moved to Australia around 30 years ago and have no Australian ancestors My parents were born and married in Formby, Lancashire, England around b1921/22 mar 1943
My fathers birth certificate has no father shown, his marriage certificate shows the name Cufflin, the man my grandmother eventually married in 1924 Leicester is not my genetic father so I am researching DNA matches to find males who would have been in the same area as my grandmother around 1920 either Lancashire or Leicestershire.
My 2 largest DNA matches have the surnames NEWBOLD & ELD
Thanks for your input
Rick