We pay 7000QR a month for an unfurnished 3 bedroom flat, and we know we are getting a really good deal for what we have. If you aren't getting a furniture allowance, you probably would need at least 9,000 or 10,000 to get a fully furnished small 2-3 bedroom flat.
Find out if you get the CASH for if they pay for your housing directly.
As for neighborhoods, there is no bad neighborhood in Doha. But, when you work with a real estate agent to find a place, they will show you places that are popular with westerners. We specifically did not want to live in a western neighborhood/compound but we had a terrible time getting the agents to not show us the places where all the other westerners live. We ended up in a western apt. building anyway. (hint: work with as many agents as you can, don't stick with one. They hate this, but it is essential to finding a place in a timely manner). So, if a western place is what you are looking for, you shouldn't have a problem. Lots of westerners like compounds since there are often pools and gyms.

They will probably tell you that rents will go down after the Asian Games, but I wouldn't count on that. The landlords pretty much see how much they can get for rent, and overall it has nothing to do with the Games... So expect your rent to go up every year. Supposedly there is a rent cap of 10% per year but there are so many loopholes it's a worthless law. You'd have to go to court to get it enforced.