Enjoy your trip to Australia, but to avoid the s......s you might want to learn some of the local spelling:

Qantas doesn't have a "u" in it. It is an acronym: Queensland And Northern Territory Aeronautical Service.

Cairns doesn't have an "e" in it.

You appear to have forgotten to go to Melbourne, an error you should correct immediately.

Sorry I cannot help you directly with your query about QF miles being of use to you. As you are probably aware, the local *A member, Ansett, ceased operations a couple of years ago and there is currently no local replacement. Scan the partnering opportunities, but as said above, the discounted QF flights have discounted mileage-earning too.