Well I'll be taking the same step next week, moving to qatar from Dubai, and I'm considering also to drive my car to Doha...I have asked the same question and here are some hints to consider:
1st, you need to de-register the car in Dubai.(car has to be fully paid off to the bank- Can't be under loan).
2nd, get an export plate, plus insurance.
3rd, you may appoint a shipping agent to deliver it to Doha, Or you may drive it there yourself.
4th, You'll need a Saudi Arabia Transit Visa To be able to drive/cross thru KSA.
Please let me know if you receive any other replies.
Thanks.