We tried to deal with this issues long back 2008, but the did not allowed to transfer the Car loan to any others unless its fully paid.

Option 1: find a cash buyer of your car and paid direct the balance to your Car, considering the buyer will agree to this arrangement.

Option 2: If the owner of the Car is not leaving Qatar, you can still continue to Pay the Car loan with internal arrangement/agreement then when the time it was completed it will be transfer the car under your name. But this option is very crucial if the owner needs to get out of the country for unknown reasons and did'nt come you have no rights to own the car and it should be surrendered to the Bank.

Better inquire with the Bank directly.