American Airlines has round-trip flights from Austin (AUS) to Sydney, Australia (SYD) for $815 with a connection. Flights October to November. Very few extended weekends available.
Priceline has “Express Deals” for about $778. With “Express Deals” the airline and exact flight are hidden until after purchase and those purchases are final. There is no 24-hour free cancellation for “Express Deals”. The flight is guaranteed to be on a major airline. Be sure to select the deal with 0 to 1 stops and a layover less than 4-hours.
San Antonio is also available, but those have really long return connections.