Finding a job in Qatar is the same as finding a job anywhere. It depends on what you can do, on luck and perseverance.
I recommend that you look at the various newspapers, bayt.com and other sites. Also do your research. You may need to change from what you studied to another field that has more possibilities (education, secretarial, etc)
However I think that it will take less time here than in the states.
If you are looking at education make your contacts now as the schools are hiring now. Otherwise after the summer. As most of the offices are almost going into siesta mode.
Good luck.