British Foreign Office's guidance for travelling to Qatar.

It is a punishable offence to drink alcohol or be drunk in public. Offenders may incur a prison sentence or deportation. Alcohol is, however, available at licensed hotel restaurants and bars, and expatriates living in Qatar can obtain alcohol on a permit system. You should not carry alcohol with you, including in your car (except to take it on the day of collection from the warehouse to your home).
You should dress modestly when in public, including whilst driving. Women should cover their shoulders and avoid wearing short skirts. You should behave courteously at all times. Any intimacy in public between men and women (including between teenagers) can lead to arrest. Homosexual behaviour is illegal in Qatar.

More good advice here