To my knowledge...one of the best Rent a Car service in qatar is - "Regency Fleets Rent-a-Car". I had rented from Regency fleets couple of times and they had very lenient and safe procedures while lending a car for rent.

Regency Fleets Rent a Car - Tel: 4554046
This number above is from the card they gave me...

I would say its an awesome place to deal with. VERY TRUSTWORTHY.