I wouldn't know about what or what isn't part of the Commonwealth, not being an Australian, but I'll wager a guess anyways. Is it something by Matthew Hindson (since he has been mentioned)?
Oh...then here's a list ^^
https://en.wikipedia.org/wiki/List_of_members_of_the_Commonwealth_of_NationsNo, not Hindson...the excerpt is too civilised to be a Hindson piece, although most of the piece is exciting in a random way.
Some Aissues off the top of my head -
Grahame Kohne, Brett Dean, Larry Sitsky, Brewster-Jones, Richard Meale, Richard Mills, Peggy Glanville Hicks, Roy Agnew, Nigel Butterley, Anne Carr-Boyd, Elana Kats-Chernin
Wow...that's a lot of names...but no, none of them, sorry...
...btw Peggy Glanville-Hicks? She's an enjoyable composer to listen to I think! (easy listening to you, retrouvailles

) Played a flute + piano work a few years ago by her...
I'll guess that the piece is by Andrew Ford or Roger Smalley...
...no...but like them, this composer did write the commissioned for the Sydney International Piano Competition one year. And the composer wrote at least another piece for another international piano competition in a British commonwealth nation...and the excerpt I posted is actually from that piece

Though not sure what you mean by supposedly Australian
Ah, you noticed that...I said that because this composer is one of the very few, if not the only, Australian composers who is not based in Australia. Actually, you know, I'd wager that this composer is about the only one, along with Carl Vine, whose works regularly get performed outside of Australia (although piano-wise, not as much as Vine. I think this composer is actually more known for his choral music in the States for example, whereas Vine's orchestral works are not as well-known as his solo piano works).
The excerpt I posted earlier was from the end of the piece. So, how about an excerpt from the beginning of the piece?