Tinabina, Alicat is right about the sponsorship situation.

Concerning work, I’m not in your same field but personally I don’t think coming to work in Qatar is a good career’s move in general, of course there may be exceptions. If you really like what you do in London, your job, your career’s prospective etc than be careful ... you won’t need just a job here but rather something that can give you good, “resell-able” experience, if you know what I mean.