You can date, but be discreet in public! Being from the Philippines, you may be under scrutiny more than a Westerner. Except for your trusted friends, I would tell people you are married if asked.

You can be taken to court for illicit relations even if they only suspect you are doing something inappropriate. Usually in these cases the accused is found not guilty because there is no evidence, but under Qatari law even if you are found not guilty, you will still be deported. There are many cases like this reported in the Gulf-Times.