Dress
As a Muslim country, there are a number of religious laws which should be obeyed by everyone in Qatar, although few foreigners seem to actually follow them. A large percentage of the local population is foreign, many of whom come from Europe, North America, India, and the Far East, so local religious dress and dietary restrictions have little meaning to these non-Muslims.
The locals dress very conservatively as they cover themselves entirely with loose fitting clothing so they reveal nothing. The men generally wear all white outfit called a dishdash and a white keffiyeh or head scarf. Foreign men are not required to imitate this local dress, although men are expected to cover up, meaning everything from the wrists and ankles up should be covered. The local women tend to wear black with a head covering, but rarely do women in Qatar cover their faces. Likewise, foreign women are not expected to imitate the local dress, but should again cover up from the wrists and neck and are best to also cover their hair, although there is no pressure to do so.
Despite these rules, which any culturally sensitive visitor should follow, the locals are quite forgiving. Generally speaking, the locals dress one way and most foreigners dress in whatever way they want. Most visitors and tourists to the country wear shorts and short sleeve shirts, which the locals are tolerant of, especially on beaches and in resorts. Although following local dress isn't necessary, covering up is greatly appreciated and respected by the local population and by visitors from neighboring Muslim countries. Having said that, there is no real expectation that a foreign women covers her hair and doing so may get more odd looks than not covering her hair.