The iPhone is not officially sold in Qatar, but when it does become available, it will be through Vodafone. I have been told by local Vodafone reps that the iPhone may be coming this fall, or maybe December, or maybe later, insha'Allah.

http://www.apple.com/iphone/countries/qa/

If you're impatient, you may have to buy your iPhone from another country, such as the UAE, and possibly need to get it unlocked.