Importing car from UAE is very simple and easy.
Make Export number plate from UAE (Dubai Traffice or whichever city the car is registerd in UAE) for Qatar.
After getting Export number plate .. you have 2 options
1) Drive the vehicle by yourself to Qatar Border (you need to have residence permit)
2) If you don't have residence permit, you can ask any road transport (cargo) company to get you car cleared from UAE/ Saudi and Qatar Customs from the borders and deliver your vehicle in the Industrial area or at your / your friend's residence address in Doha, Qatar.
3) The custom duty of Importing a vehicle is 5% of the value of the vehilce.
4) Cargo Company will charge Dhs. 1500 - 2500 for transportation only. Transport charges vary from Company to Company in UAE.
5) You can also ask the Cargo Company to to pay all the cost of Custom clearance and deliver your vehicle in the City (Doha). else you have to go to Qatar Border to pay for the Custom duty and drive the vehicle yourself back to doha.
6) Qatar border is almost 100 kms from the Doha City.
7) You will get insurace of QR. 100 for 2 weeks to drive the vehicle on the Export number plate in Qatar.
In short you cannot bring the vehicle on your name while you are on a Visit Visa. You must have residence permit to Import the vehcile in Qatar.
If you have RP, and once your vehicle is arrived in Qatar, you can drive the vehicle with your UAE driving lic. for 2 weeks only since the insurance you will get from the border is valid for 2 weeks. After which you must register the vehicle with Doha Traffice dept.
Hope above is clear. If you still have any query or clarification please feel free to ask :-)
SPEED