I'm not sure of it's allowed or not, i'm here few days ago, and live in La Cigale hotel, which is a wonderful hotel, i recommend it for you,
price is 1000/night with pick up from airport and dropping too,
it has nice view, and music hall,
others i have no idea, but i'm exploring, first impresion Doha is very beautiful and clean, people are friendly and optimistic,
I feel the growth is very fast in this country,
Good luck