Living in Qatar is not a problem for a foreign woman.
You just have to be a bit careful what you wear when you go out to public places, specially malls.

Other than that, it's a simple life. As for work, Event Management is not a very happening thing in Doha, but I am sure that you will be able to find work in Hotels.

If you need further info, please do not hesitate to contact me!

Cheers!