No it is not illegal to sell a car with a RWC, when your buying private your buying 'as is', you have no guarantees.
Is the car still registered in NSW? If so, i think you have about 14 days to have the car re registered in QLD to QLD standards and in your name. If the rego has been pulled off the car you need to have it inspected for rego ASAP.
Im sure that a NSW RWC is irrelivant in QLD, so its really only to let you know the car is sound.
I live in NSW, and recently bought a car from QLD, unregistered. I needed a permit from QLD to drive the car out of the state and a 2 day third party insurance from QLD. I had the car registered to NSW standards the next day, which required a full inspection to be able to be NSW registered.
Now the car is in QLD, it needs to be fully registered in QLD from scratch, anything to do with NSW is now irrelivant. I dont know the proper terms for QLD as I only know NSW rego laws.
I hope that made sense!
EDIT:
Here is a part of the Queensland Transport website on Vehicle Registration, might be more help than Ive been!
http://www.transport.qld.gov.au/Home/Registration/Motor_vehicles/
EDIT:
Like I said before, when buying a car privately you are buying the car 'as is', there is no warranty with the vehicle, so to answer your question, no the seller doesnt have to supply a RWC nor does he have to fix the car, you should have asked to see the RWC before handing over any cash or had a mechanic inspect the car before buying it. Unfair I know, but once you hand over money for the car, its your problem, even if the ad says something different. I learn this the hard way.
No you dont need a RWC to sell a car in NSW, but its going to help sell it if the new buyer can see its been mechanicly inspected and passed. NSW have much more thorough vehicle inspections then QLD.
Once the car is sold in NSW, you should have filled out the back of the vehicles rego papers before you handed over money. You took half, the seller took half of the rego paper. Both the buyer and the seller take their pieces to the NSW RTA. The seller gives his notice of disposal, the buyer his notice of new ownership of the car. Then the car is transferred into your name and out of the sellers name and full responsibility, giving you 14 days to have the car registered into your name, in your case, into QLD.