Southwest has round-trip flights from Austin (AUS) to New Orleans (MSY) for $98, NONSTOP. $49 each-way. Flights March to April. Origin/Destination reversible. Weekend availability. Availability in April is limited to mostly midweek.
Monday, Thursday, Friday, and Saturday departures are available for $10 more.
Carry-on and checked bag are allowed for free. Southwest doesn’t charge change fees.