Hey newboy2, unfortunatelly there is nothing like that in this country. There are a couple of web site with pictures, but they have been the same for months!
The way that I found my appartment was to pick up the peninsula newspaper and phone those guys. You will see that even the adds on the newspaper are the same week after week. You need to call them and explain them what are you looking for.
Be ready to answer the questions about which area is better for you, what are your requiriments about number of bedrooms, etc (don't forget the shaded parking) and the budget that you have.
They will then call you back (or no and then you have to call them again) and give you some directions and time for a visit to a place. It's a hard way to start wandering around the city and learn your ways... so that means that you need to rent a car...
I've been recently for this process (actually in september) so don't hesitate to ask me any question that you could have.

Welcome to Doha! After the first turbulent month everything will be fine :)