You may need to confirm with your customs agent in Dubai, on importing cars older than 5 years ,if you can, follow the below procedure

1) Get export number plates from Dubai RTO.
2) Letter from your employer/sponsor in Qatar allowing you to bring the car into Doha on account of your employment.
3)Get from your car dealer a GCC statistical report showing the car/engine number against the duty paid. This should save you from paying duty again.
4)Provide copies of your passport/visa and declaration from your employer to your transporter.
5) when the car arrives in Doha, get technical inspection done( like your tasjeel in dubai), get insurance and go to the traffic dept in Madinat Khalifa with another letter from your sponsor stating no objection to getting the car registered along with the "computer card" to verify his signature!
6) Get the application form typed in Arabic , attach the ,export number plates,technical report, insurance document, letter from sponsor, and I think QR400 for new number plates and registration.
Voila! it should be done.
hope this helps!