This is what I found out today about exporting a vehicle from the UAE to Qatar.

1. Thirty days prior to your planned departure, go to your insurance company to set a cancel date for your insurance. Set the date to a few days after your planned departure. You should get a prorated refund for the unused portion of the insured period.
2. Twenty days or so before your intended move, take your vehicle to an inspection center for an export inspection. Pay 120AED. If anything needs repairing, get it repaired and return to the inspection center. One retest is free within 30 days of the initial inspection.
3. A day before you intend to physically leave the UAE with your car (or the morning of departure), go to the inspection center again and pay 300AED for export papers and 50AED for blue export plates.
4. Pay 100AED for four days of export insurance. You now have four days to get the car from the UAE to your destination.

sankarguhan: Most likely I'll be working in Doha for September and October awaiting my RP. Even if I were to to ship my car via road cargo, I still would not be able to insure and register it in Qatar until I had my RP and Qatari ID. My understanding is that the export documents and export plates allow me to drive the vehicle to Doha, where I will have to find somewhere to park it for two months or so, while I wait for the necessary Qatari documents.

Another option is to find someone I can trust to insure and register the car for me, though I believe that it would still be illegal for me to drive a non-rental vehicle in Qatar without an RP. That's the way it works in the UAE, though many people do manage to drive non-rental vehicles on only a work-entry visa for the first month or so they are in-country.