I've never heard of any Westerner doing this and haven't seen any non-GCC numberplates on the road. Qataris often import cars from saudi and UAE, but they're GCC countries and it's overland, whereas you're presumably non-GCC and thinking of ships. Try going to http://www.moi.gov.qa/English/Inquiries.htm and writing a letter. And report back here if you ever get a reply.