There are a lot of good places to take pictures, like parks, beaches, cournich, Shopping Malls, Zoo etc. But as mentioned above, and it is everywhere in the world, you have to avoid taking photos of government buildings, security installations and armed forces areas. Also important is not allowed to take any picture of the Gas for Fuel plant in Maisaeed or Ras Laffan areas, but dont worry you cannot enter there without security pass and no need to go there also.
Anyway at general there are no restriction on photography in Qatar.