I don't think that there is any problem in bringing any car from US to Qatar.

People use to buy vintage, classic and muscle cars of 60s and they ship them here. What i know they use to have their vehicles shipped here thru ebay.

I know one garage in Industrial Area, its name is EZDAN GARAGE, Street 26 and the guy name is Hassan Laal, he is a Qatari guy who loves classic cars and use to ship them here.

By the way, nice cars dude..