Both UA and AA will interline bags to QF. As you're booking on separate tickets you'll need to have a copy of the e-ticket with you when you check-in, and you WILL need to pay for the bags on the ORD-LAX leg (unless you have status).

Southwest is definitely a no. Virgin America also flights ORD-LAX - not sure about their interlining.

In either case make sure you leave yourself at least several hours in LAX. No matter what the airline ORD-LAX stands a change of being delayed.