I flew in Qatar from 2008 to 2010 with the Qatari Aviation College (which was actually in existence as part of Qatar Airways to train their ab initios) to maintain my currency whilst I was working on the new airport. Subject to the usual letters of approval from my employer, there were no difficulties but of course being able to do anything was time consuming, required many approvals and was treated as a big, big, favour being done to me. Airside badge was fairly easy come by, subject to the usual bureaucracy and there were other nationalities light airplanes on the College / GA ramp. An American guy kept an N reg Cessna 337 there and his "bimble" was Bahrain and back. There were restrictions on QAC aviation when the temp was above 40 C, which meant only mornings in the summer. There were frequent disruptions to booked flights due to VVVVVVVIP movements.
Aeroplanes were Archers with less than Warrior performance due to the number of horses just driving the A/C.
I got a Qatari PPL on the basis of my JAA PL but it was only valid for 6 months and (weirdly) didn't permit solo flight. Not exactly a 61.75. Qatar refused to recognize my JAR PPL for either Qatari airplanes or use in Qatari airspace unless accompanied by a Qatari licensed pilot.
If you have serious aspirations to learn to fly, stay current and base an aeroplane there which you get serviced elsewhere all I can say is best of luck. The fuel should be cheap though.