Don't know if you still need a response...
They won't let you check your luggage just to DAL.
When you don't show up for the AUS flight, they may consider it a security risk (you're not on the plane but your luggage is) and you may have big problems. Or they could miss it and your luggage could go all the way to AUS on that flight and sit in the baggage claim area. Either way, probably not a good idea.
Can you ship your luggage?