Falcon2000easy,
Why not apply? Your 737NG time will be valued - not sure if you need a specific number of hours on that aircraft (i.e., 1000 hours minimum). I am sure someone else has that minimum number.
That said, I would drop the "Falcon 2000 Easy is more sophisticated than the space shuttle" line. If you can fly a 737NG you can fly a 777.
QR is hiring big time as well. Doha is very different from Dubai but the jobs are similar. Plus, who knows, perhaps at QR you would get a seat on the 787 (coming in June) which is "almost" as sophisticated as a Falcon 2000 Easy...