Hmm, I do know that you cannot hold two GCC RPs at the same time. You would not be coming into Qatar with a Qatar RP, it takes about a month here to get one. But you would probably have to fly back to Kuwait to get yours cancelled in your passport but you can't leave the country while your RP is being processed. Sounds like I've convinced myself it would be easiest to have you sponsor cancel your Kuwaiti RP before you come. Your employer will send your entry visa to you.
Mandi