pacific, yes AA's 75,000 partner award allows you the stopover in a gateway city (and an open jaw, if you want one). So you can make Cairns your final destination, from which you would return to your starting point in the US as part of the 75,000 award. No additional ticket purchase necessary for that.

A quick check of award availability, and I only checked LAX-SYD-LAX on Qantas, shows all kinds of dates with 2 economy seats available early in December, and then Christmas Day. Return looked a lot tougher, unless you want to go on Christmas and stay a month. But I did not check any of the many other options, including Qantas flights from BNE and MEL, Qantas flights to SFO, or the other partners.