living in Qatar: I'm obliged to work?

Well you didn't mention if you and your partner are of the same sex or opposite.. If opposite then you have to get married and stay together but if you are gay then you can stay together but you definitely cannot get married because same sex marriages are not accepted here.

You can come under a visit visa or tourist visa. To stay much longer you need to have a family visa or a working visa. Either way, you cannot stay in the same house with your partner without a valid marriage certificate. Else, you and your partner will only invite yourselves to jail-time and possibly, deportation.

Depending on your nationality you can come in on a tourist visa, but in order to stay you have to be sponsored by a parent, child, spouse or employer.