Maria, your best bet is an apartment/villa share. Great way to meet people and will make your stay in Doha far more enjoyable. Not easy to find these and generally are posted in FB by friends. Try http://qatar.dubizzle.com/en/property-for-rent/rooms-for-rent/search/
There are some good options on there. I'd recommend West Bay, though it's a more expensive. It'll be a much easier transition for you there.
MM is right though, check Ezdan Hotel and Suites in West Bay...not amazing, but good for a short stay and have some ok deals. There are a lot of areas you should stay away from, so do your research!!
Good luck, and I'm sure you'll have a great time in Doha.