Delta, American, Alaska, and JetBlue have round-trip flights from Austin (AUS) to Los Angeles (LAX) for $77-$85, NONSTOP. Flights October to February. Extended weekends available. Origin/Destination reversible.
Carry-on bag is allowed for free on all airlines listed except JetBlue, which charges a fee. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.