Technically, your car is still owned by the finance company or bank (there is a mortgage on it). Normally they will not allow the vehicle to leave the UAE until such time as that mortgage is cleared.
Speak to your finance company and see what arrangements they have in Qatar to be able to transfer the mortgage to that branch. At this point you can then get into the paperwork nightmare. You must first de-register the car in Dubai, obtain an export certificate and set of blue plates for it and THEN you start the problems. As soon as the vehicle leaves Dubai, you need an import certificate for Abu Dhabi, an export certificate to Saudi Arabia, an import certificate for Saudi, an export certificate from Saudi to Qatar and finally an import certificate to Qatar.
Easier option: sell the damn thing here. Buy a new one in Qatar!
Knight