Delta and KLM have round-trip flights from Austin (AUS) to Dubai (DXB) for $784 with a connection. Flights in March. Departures on Monday, Thursday, and Saturday.
Limited dates available.
There is a long 6-hour connection in Amsterdam on the return flight.
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.