Althogh I would definately consdier private flying here int he UAE, the problem is, where are you going ot go!???
The way I see it is that it'd be quicker to drive then it would be to get to the airport, prep the plane and fly there.
However, if it is a Pitts, then maybe your intentions would be just to have a block of airspace close enough to the airport to roll, loop and try and bend that Pitts!! ;-) In that case, look into the Umm Al Quwain Flying Club. It's a private field, they have a flyign school there and parachute club.
As for local help on the Pitts, let me know, i know a guy.
I'd be intereted to know what you learn and what you decide. It be great to see a Pitts in the area.
Good Luck!