I just came to Doha about 1 month, I was in Kuwait 2 years. I did not see any problem like U said while I was there..women wearing the clothes that they like to wear even short and Tank top..even people not so happy to see maybe..but they do that..

I have many friends that not wearing abaya muslims and non muslims..They have no problem with clohtes.but it is still better to follow the custom in the country U stay at..

Doha hummmm don't know so much but I think not so much like Dubai..Good luck in Qatar...