I am flying from ASE-LAX on United and then connecting onto QF 94 to MEL.

I am flying from ASE-LAX on United and then connecting onto QF 94 to MEL. Can I check my baggage through from ASE-MEL or do I need to recheck it at LAX given that Qantas and United aren't partners.

It depends. If your ticket is a through booking with both carriers, then you're able to check through as QF and UA have an interline agreement. If however the UA and QF flights are on seperate bookings/tickets then you will have to collect bags at LAX, cart it all the way across to TBIT to check in at the QF counter. 

If you're Gold/Sapphire Platinum/Emerald with QF/OW, you might be better off short checking your bags to LAX since UA is not able to put QF/OW priority tags, and any Star Alliance tags attached from ASE would have no cred with MEL baggage handlers. 

Thanks, that helps a lot!