Yes, you will be able to find a single bedroom independent accommodation within the budget you have stated. Try searching for a studio apartment and a good place would be Qatar Living. But if you desire to live around West Bay or The Pearl, then of course you may find housing there on the costly side. Those are areas for the "white horses," hence the high rents. There are many other areas in Doha where rents are reasonable and which are quiet.
As for the negative statements with regards to Doha, each city or country in the world has its good and bad qualities. Doha has many good sides to it. But then there are people who live here, earn here, pass decades here, and then still turn around and criticize the city for not allowing them to do things they could do freely back home.