Qatar is a very interesting middle eastern country. Let me start out with telling you that actual Qatari citizens make up not even half of the coutry's population. The majority of the population is from places like Sri Lanka, the Phillipines, India, other arab countries and some europeans. The work force of the country is made up of the foreign nationals, not the locals. Because of the population mix just about everyone speaks english. The Qataris usually wear the traditional dress, the Abaya for the women and Thobe (it is not called "the white dress") for the men. The men either wear the white head covering or the red and white checker covering. Not all of the women cover their faces, but some do. You will see muslim womean who wear typical clothing and only wear the Hijab (the hair covering) Because there are so many other nationalities that make up the population in Qatar you will see people in traditional indian clothing and western clothing. Despite what you may see when you get there it is best to dress modistly (it is a Muslim country). Women, wear long skirts or pants. Its not a good idea to "show leg". T-shirts are ok, but a 3/4 to full leng sleeve would be better. Whatever you wear just be modest and keep your shoulders and chest covered. Men, jeans or slacks and polo shirts, dress shirts, t-shirts will do you fine. At the hotel pools and beches it is ok to wear your bathing suit, just be sure to cover up when you leave that area. Generally the Qatari people are very nice. All you need to do is show that you respect their culture. It never hurts to learn the basics (Thank You- Shukran, Your Welcome- Afwan, Hello- Marhaba) in Arabic before your trip!
In Qatar you will probably see some expat residents wearing anything from shorts to spagetti-strap tops. While most likely no Qatari will ever tell you that you shouldn't be wearing this, that does not mean that they don't take offense to it.
Consider what the Qataris themselves wear - both men and women are completely covered from head to toe in loose, nonrevealing robes, and additionally for women the face is often covered by a veil as well. While I'm not suggesting a foreign women should wear a veil or even cover her head, it is respectful to wear loose-fitting clothes that cover the limbs. You will be much better received this way, and will avoid alot of unwanted attention from men as well.
While you can probably find suitable clothes in your own wardrobe, if you want to buy something here then try the long cotton robes for sale in the shopping malls, the souqs, or even the large supermarkets such as Carrefour. I've found these to be the most comfortable thing to wear in the heat, and nowadays I often wear them at home too.
For men, while short sleeves are OK, it's really best not to go out in shorts, no matter how hot it is outside.
Unlike its neighbor (Saudi Arabia) women can drive. However, conversvatism is key. When in doubt, women should be more covered than less. It will keep you out of trouble and it shows respect for the local culture.
While you dont have to wear this traditonal Saudi dress, women should not show much, if any, skin (hotels are an exception)....head coverings are not needed for non-Muslims
Qatari people usually wear the long white dress which is typical arabic dress. but there is something very common which i ahve noticed. I noticed that Qataris Must Wear the black ring on the headwhen alongwith this white long dress.
In the Picture you can see Qatari boys from College coming out and they are in their national dress.