Qatar has strict islamic rules, compared to say UAE. But nothing over the top like Saudi. My friend works for QA. She has a 3:30 am curfew (which is fine 'cause all hotel clubs and late night places close by 3 am give or take). Also, you can't have a guest in your accomodation past 10pm.

If your walking around on the street / outside malls, be prepared to receive all kinds of unwated attention from guys in white land cruisers. But shouldn't be a problem as cabin crew are trained on how to handle unwanted attention, lol.