I think they will move it.
Too ripe a target for terrorism. Considering you can drive across SA to get there in a few hours from Yemen.
this is from the gov.uk site:
Importing drugs, alcohol, pornography, pork products and religious books and material into Qatar is illegal. All luggage is scanned at Doha Airport Arrivals Hall. DVDs and videos may be examined and censored. Penalties for drug offences are severe, often resulting in prison sentences.
It is an offence to drink alcohol or be drunk in public. Alcohol is available at licensed hotel restaurants and bars, and expatriates living in Qatar can obtain alcohol on a permit system. Don’t carry alcohol around with you (except to take it on the day of collection from the warehouse to your home).
You should dress modestly when in public, including while driving. Women should cover their shoulders and avoid wearing short skirts. Any intimacy in public between men and women (including between teenagers) can lead to arrest. Homosexual behaviour is illegal in Qatar