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To redeem AA miles for travel on QF, you must call AA -- not QF -- and pay the telephone-ticketing fee (in addition to the close-in award fee). It is not possible to book QF award flights online when redeeming AA miles.
One-way between Australia and North America costs 37.5K AA miles in Coach.
You can find all three of AA's award charts (zone-based AA metal only, zone-based Partner, and distance-based "Explorer") at aa.com under the "AAdvantage" tab.