Hi there.
I'm a muslim UK ex pat female, been in Doha about seven months... My opinion from what people I know have said/experienced is that it wouldn't be looked upon well, and may cause you some grief if anyone suspects anything untoward (which of course would not be the case) but they will read into this (as people do...) - as the women here are quite segregated from men in general terms, so even though you/I would not bat an eyelid at this knowing its perfectly innocent - the culture here is a bit different. I'd advise you try to find a villa share with other women, though I'm not sure how easy that will be. Best of luck.