It doesn't make any difference if you are a westerner or not if you live in a muslim country you have to live by their rules and respect their beliefs.
I am from the UK and living out here with my husband. We brought our wedding forward just so we could live together out here.
Open displays of affection are frowned upon even when you are married. If you cant keep your hands to yourself in public Qatar is not the place for you.
Alot of couple do co habit over here and are discreet about it but it is illegal and if you are caught you will be deported.