If it's the part of the world you're worried about I wouldn't be all that concerned. I've just spent the last 5 years living in the middle east and will probably be going back in the near future. I don't have any hesitations about doing so. I think living in Qatar would be a wonderful and unforgettable experience for your daughter. As Tyra said, what exactly are your concerns about letting her go?
When I stand before God at the end of my life, I would hope that I would not have a single bit of talent left and I could say “I used everything you gave me.”