Southwest has round-trip flights from Austin (AUS) to New Orleans (MSY) for $118-$138, with a connection. $59-$79 each-way. Cheapest flights are midweek, with weekend dates about +$20 more expensive. If you’re traveling with multiple people, you can save a little more by buying the $250 Sam’s Club gift-card which is on sale for $239. Flight availability is usually between September to November. Origin/Destination reversible. No major holiday dates were found.
A Carry-on bag, two checked bags, and also a personal item is allowed for free on Southwest.