Requirements ????
Let us engage an Event Mgmt company and arrange red carpet from Airport to your house....also declare a national holiday.....lol

just kidding .... if the BA flights are cheaper, let her come by that flight. As a UK citizn, she is entitled to get "visa-on-arrival" from the Doha Airport.

Staying together with a girl friend is illegal in Qatar. But arranging her a hotel for 10 days also going to be a costly affair..I will advise to be a "low profile" when you move out with girfriend. Not to show anyone it is your GF. not to even your neighbours. dont provoke anyone with your actions in public. then you can manage 10 days.