There is one liquor store, Qatar Distribution Centre, in Doha. To purchase things there, you must have a license that can only be obtained by having a written letter of permission from your employer. You can only get a license when you have obtained your residency permit and you will need to get a letter from your employer confirming your salary in addition to paying a deposit for QR1000. The selection is good and is like any alcohol selection of a large supermarket in the West. Prices are reasonable although not cheap. Alcoholic beverages are available in the restaurants and bars of the major hotels, although they are pricey. As far as non-alcoholic drinks go, be sure to hit some of the Indian and Middle Eastern restaurants and juice stalls. They whip some tasty and exotic fruit juice combinations that really hit the spot.
It is forbidden to bring alcohol in to the country as a tourist; at Doha airport customs xray bags and will confiscate any bottles of alcoholic drink. They will issue a receipt valid for 2 weeks to reclaim the alcohol on exit from the country.