For AS - just book through their website. It's easy and you just enter your QF number in the booking process.
For AA, it's a little more complicated. With an Australian card, you have to use the Australian AA site - the catch is, often the Australian site is more expensive than the US site (sometimes hundreds of dollars more).
I recommend checking the fare in google flights as it uses the US pricing but converts it into AUD. Then compare to what the Australian site says. If it's about the same, book through the Australian site.
If google flights is cheaper, click on the "Book with AA" button. This will load up the AA US site, and you'll now see the fare in USD. Complete the check out process, but when it comes to payment, select the "Hold" button.
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This will generate the booking (unpaid) and give you a record locator (booking reference).
Then simply call the Australian reservations number (02 9101 1948) quote the reference and ask to pay with an Australian card. It's a good idea to offer to pay in USD, otherwise they will convert to AUD and you will pay more than your bank will charge you for the conversion.
You can fudge your address on the US site and use a US zip code with your Australian card, but the above method is how you do it legit.
@AFF Editor, when you've run out of popcorn stories
- might be an idea to make an article on this process, it's coming up very frequently lately.