I know this thread is old but anyway,

Only Qataris has the power to buy weapons. We sell crossbows, bows and (rifles/shotguns before in villaggio). We always ask for ID's before we let a customer take a weapon.

Resources:
I'm working in a hunting company "Thawab hunting" formerly located in Villaggio now in Souq Waqif/falcons compound.
www|facebook|dotcom|/thawabhunting