If this is your first trip to Doha you probably wouldn't want to drive here anyway unless you are very brave. Before I took the plunge and got a car I used a driver called Ahmed tel: 5496293 who I found very reliable. He has a decent car ( a late model Chevy) and is reasonable on cost (around 15QR a trip).

As far as the job is concerned, you could use this trip to visit companies and talk to them. They may well be prepared to sponsor you. You then reapply once you have left Qatar.