From what I was told in Doha, crime is minimal. This is not entirely due to the existence of Sharia (Islamic) law, which in Qatar is applied only to Muslims anyway (as distinct from Saudi Arabia, where it applies to all in the kingdom). There are other factors, such as the fact that most Qataris are reasonably affluent, if not downright wealthy. As for foreigners, most European and American expats are professionals on lucrative contracts, while the Indian and other population (the bulk of the population) are in Qatar to work and build a modest fortune so that, after some years, they can retire to their home countries as (by local standards) affluent people. No-one wants to be deported!
Travellers must remember that Qatar is an Islamic state therefore they must abide by their laws.
Women must dress conservatively away from the beach etc. Pork is not allowed in the country. THERE IS NO PUBLIC TRANSPORT AS SUCH BUT TAXIS ARE VERY CHEAP