Do women in Qatar have to wear an abaya when out in public?

Women in Qatar have a lot more rights than in Saudi Arabia and the Gulf state is definitely not as strict as Saudi. Women can drive and expat women are not expected to wear the abaya - although you should still ensure that you dress conservatively and modestly when out in public - this will also help to avoid attracting any unwanted attention. Read more about what to expect in Expat Arrival's Women in Qatar page, and the Culture Shock in Qatar page.

Qatar is definitely more lenient that Saudi Arabia - as a woman I'd much rather go there.

When you mention that the ladies of Qatar have 'more rights' than the women of Saudi - you have to understand the religion a bit. There is no such thing, from an Islamic point of view, as 'more rights'. It is any Muslim woman's obligation (despite nationality) to dress modestly in public (ie. wearing abaya/loose clothing/nothing tight). In any Muslim country this obligation still stands because it is part of the teachings of Islam. Whether people adhere to this rule is another thing. Now, in Saudi they try to uphold this obligation for the betterment of society, being the centre of Islamic culture and heritage. However it is a Muslim lady's right to choose if she wears Niqab or Hijab. Hijab (headscarf) is compulsory, however it is not against the 'law' for a woman not to wear it, although it is required by her religion. In Saudi the government wishes the society to uphold the Islamic laws as purely as possible, thus ensuring a stricly conservative society. Saudi Arabia is not a secular country and the religion and state are not separate like other countries in the Gulf, thus the reason for these 'rules'. If you want to live a more secular life don't visit the 'pure Islamic' countries of the Middle East at all and at the very least try and learn something about the religion of the country you wish to live your life in before you go - research it from the source ie. religious scholars/reputed Islamic websites that can explain everything to you. Stop spreading half truths and non-facts in forums like these where you don't even end up with the right answer to your questions in the first place and then still proceed to visit these Islamic countries, still full of as much ignorance as you held before writing on these forums. If you cannot possibly live without showing off your cleavage/bare flesh etc. for a while then just simply DON'T GO !!