Delta has round-trip flights from Dallas (DFW) to Sydney, Australia (SYD) for $912 with a connection. Flights April to May. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required. The outbound connection in LAX is about 5-hours.
A Carry-on bag and also a personal item is allowed for free on Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.