Hello,
well i don't know about car shipment, but i do of a company who ships your stuff (i shipped my stuff from dxb to doh) it is called "city moon" and sadly i only have their dxb number which is +971 4 2355 135 or +971 4 2355 136
thanks and best of luck moving to dxb (trust me it is much more nicer in every way :) )