The problem I find here with renting a car is unlike most countries, in Qatar if you rent a car with insurance you still have to pay a minimum of QR 1000 if you have an accident and its your fault or if the other driver has run away.  With the amount of reckless drivers on the road, I'm even worried to park my rent a car in a public parking place.  

Taxi's are like gadarene said very difficult to find on the roads and if you call a cab, you must call a day in advance or on busy months, 2 days in advance!!!

I used to drive in UAE and I agree Qatar drivers are a lot reckless but not so much different from UAE. But I come from India and I have seen total madness on the roads there so Qatar to me is soooooo much better than my home town.  :-)