Hi
You can play with fairly well opponents who are frequent visitors of chess Federation located at QNOC building (Al udaifi tower) West bay 13th floor. Guys there are interested in playing blitz chess only. so be prepared to play blitz 5 minutes!.
Also Qatar chess federation arranges Open chess tournaments every year. I got 4th place this year.
visit www.Qatarchess.com also for more info.