Not being particularly conversant with the Australian systems of BMD registration and their searchability, you may suffer from difficulties in that regard. I know you don't want instructions on how to research, but my own experience is that very few even relatively close DNA matches will have recognisable surnames from the direct lines of my family tree, due to the number of intervening marriages between the match and the generation where our common ancestors reside.
I have spent a lot of time (more so than researching my direct family probably) in researching and recording collateral lines - the lines of descent from brothers, sisters, aunts and uncles of my direct ancestors, and bringing them forward as far as possible to the present date. Sometimes this produces direct results, in that the surnames of DNA matches that I would otherwise never have recognised are already in my tree and require minimal (or no) further research to identify the matches. They also have the additional benefit of solving a lot of problems and dead ends along the way, as several times I have as a result found information that has broken down what at first appeared to be insurmountable brick walls via the paper based research involved in expanding those lines, completely unrelated to DNA matching.
But for those relatively close matches that I have which aren't immediately obvious, even if the match for whatever reason of their own does not wish to correspond with me, there is often enough information in their online tree, or otherwise, to enable me to identify them through a little further research of the England and Wales BMD records. The names of two grandparents might allow me to find their marriage, then search for the names of children born to them having the same mother's maiden name recorded, and do the same with thier marriages and children in turn. Or I can work backwards from a name that I do know, again by searching the BMD records.
I have just resolved one match where I had only her father's surname, and no idea who she was, other than that she was female. But an online search allowed me to establish that she had also used her Ancestry username on pinterest, where her proper name was also recorded against that monicker. Armed with that information, I was able to work back three generations through BMD records and find our connection

I assume from what you are saying that there is no way to perform similar searches with Australian BMD records?