Is the sector from SIN-KUL booked on a MH flight number or is it a WY codeshare?

If it is the WY codeshare then definitely no checking of bags through

If it is the MH flight number, then since it is an award ticket, I believe that QF will check bags through

Class of service has no bearing on it

Good choice of airline with WY

Given that there is no protection if you miss the onward flight, hopefully you have allowed plenty of time in SIn which would allow collection and rechecking of baggage though