I'm working for one of the major co.'s in the middle east and I can let you know most airlines over here are screaming for pilots GF, EY etc ....
I someone else has said they all ask for experience but if I was you I'd definately go to the websites of all the international airlines over here and fill out the application forms for FO positions.
I can say my co. has taken on a lot of non-rated pilots to try and fill the void b/c there just doesn't seem to be enough experienced guys around.
Good luck...