I have many, many friends that live together with girlfriends, prostitutes, etc... It is common as a Westerner to have female co-workers and live literally next door to them within the same villas. Many of them travel together, dine together, party together. As long as your not "making-out" in public and conduct yourselves appropriatly you will be fine. No one is going to go out of their way in this matter. Do you know how many people the LEO would have to stop daily to question each and every couple? It would be a waste of time unless they are doing something questionable in public. I've spent many nights with many different women out on the town in Doha and never had a problem. I've even dined with a couple Qatari men who were dating co-workers of my girlfriend. No one really cares about this stuff until you do something stupid to attract attention.