Being positive - as you have booked what you did. But assuming you miss the flight or are close.
When you arrive, you collect your bags, customs etc, and then head to the right to the Qantas international transfer desk.
There are a series of checkin desks, I would simply go up to the business one, or which ever is free, it does not really matter, and say that you were on AA73 which landed late and believe that you have missed QF04xx to MEL.
Show your AA BP and the itin or BP for the QF flight.
They are more used to missed connections and have a degree of flexibility that you will not get in the domestic terminal or over the phone. They know that people mess up the bus time from one terminal to the other etc
I expect that they will change you for free, or at least waive the fare difference and then just the change fee of AUD 90-99?
Just be polite and smile - self importance does not work well down here
Smile and say thank you :-)

Let us know how you go.

KF