There are a number of car rental outlets (some of the international ones like Europcar, Budget, Avis...)at the arrivals hall in the airport. I would book a car in advance because you never know if they have a car available or not when one arrives. Of course, the high end cars are almost always available but economy car need to be booked in advance. You book these on individual company web sites. The link below is Europcar's:
http://www.europcar.com/airport-DOHA.html

If you are visiting a friend or a company, they can also arrange a rental car for you.
good luck