.. I am planning to do the same thing but from opposite side. To bring my car from UAE (Abu Dhabi) to Doha...
Selling under pressure is not my option. Will loose money so I made my mind to bring it here. Shipping is to bloody expensive, can go between 3k – 7k.
Advice given to me was. Get the new residence visa firs that go back t your old place and then drive the car. You can expect no or significantly less problems like that.
Custom should be waived if you have all necessary papers that car is bought in Qatar and that custom is paid. (GCC is customs and trade union)
SUGESTION: Why don’t we just swap… 

Question for all: What is the “red tape” mentioned couple of times by some ppl above.