Even if they could do it, I doubt AA would risk pissing off Qantas (No U. The code is QF, not QA, as well.) and fracturing OneWorld.

QF might not hate DFW-SYD- though they wouldn't like it-, but AA starting LAX-SYD would make them very, very mad.

Not to mention that a 5th airline on that route would absolutely ensure none of them made a dime on it.