I managed to book two first class awards on Qantas, Dallas Fort-Worth – Sydney and return, on the exact dates I wanted. The flights did not show up at AA.com but American agents had no problem seeing the space when I called.
I’ve booked a lot of awards but I’ve never had occasion to book an infant through AAdvantage against a Qantas first class award. So I was surprised when successive agents told me it wasn’t possible.