Originally Posted by
inasmuchas
Not a dumb question at all.
You can take the QF flight from LAX-JFK (or JFK-LAX), provided you are connecting to or from a QF trans-Pacific flight, such as you are proposing with SYD-LAX.
I'm fairly sure it will need to be on the same itinerary or booking reference, but others may be able to confirm that.
You do not have to be connecting. Qantas do require your PNR contain a transpacific segment on QF, but that's it.