Please see what wikipedia says about Qatar's Law:

Qatari law
When contrasted with other Arab states such as Saudi Arabia, for instance, Qatar has comparatively liberal laws, but is still not as liberal as some of its neighbours like UAE or Bahrain. Qatar is a civil law jurisdiction. However, Shari'a or Islamic law is applied to aspects of family law, inheritance and certain criminal acts. Women can legally drive in Qatar, whereas they may not in Saudi Arabia and there is a strong emphasis in equality and human rights brought by the HRA.

The country has undergone a period of liberalization and modernisation during the reign of the current Emir, Hamad bin Khalifa Al-Thani, who came to power in 1995. Under his rule, Qatar became the first Arab country in the Persian Gulf where women gained the right to vote [18] as well as holding senior positions in government. Also, women can dress mostly as they please in public (although in practice local Qatari women generally don the black abaya). Before the liberalisation, it was taboo for men to wear shorts in public. The laws of Qatar tolerate alcohol to a certain extent. However, public bars and nightclubs in Qatar operate only in expensive hotels and clubs, much like in the UAE, though the number of establishments has yet to equal that of UAE. Non-Muslim expatriates resident in Qatar are eligible to receive liquor permits permitting them to purchase alcohol for personal use through Qatar Distribution Company, the exclusive importer and retailer for alcohol in Qatar. Qatar has further been liberalised due to the 15th Asian Games, but is cautious of becoming too liberal in their law. Overall Qatar has yet to reach the more western laws of UAE or Bahrain, and though plans are being made for more development, the government is cautious.