Delta has round-trip flights from Dallas (DFW) to Sydney, Australia (SYD) for $797-$847 with a connection. Flights January, February, March, April, July, August, October, and November. Departures on Monday, Tuesday, Wednesday, and Sunday. No Thanksgiving dates.
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.