Does AA permit paid domestic F passengers into their lounges? I think not. As has been pointed out, QF permit business class pax into their domestic lounges if part of an international itinerary, which is more generous than AA where they only permit access if on a same-day international connection.

Also note that on a business class OneWorld Circle Pacific fare, if they had joined the AA Platinum Challenge they would have had AA Plat status (and hence OneWorld Sapphire status) before they reached Australia and hence had access to all Qantas Club lounges along the way through their newly acquired OneWorld Sapphire status.

And also note that Qantas does not discriminate as to how you got the business class seat. For international flights, lounge access is provided not matter if it is paid, award, upgrade etc. If you have a business class boarding pass for the flight, you get lounge access (international and domestic on the same itinerary).