Ok.....
Al Khor field is a strip utilised for GA, mainly by the college.
In order to use it, you need PPR from the QCAA.
In case your airplane is forreign registered, you are NOT allowed to overfly the country!
There are a few privately owned airplanes, mainly belonging to Big Sheikhs. There is one Canadian who has a Doha based push pull airplane, but he knows the place very well and even he is facing trouble.
So GA in Doha, slowly emerging but far from serious!