With a Dispatcher's license from an ICAO member nation, provided that a UAE employer makes the request to the GCAA, you can convert to a UAE GCAA Dispatcher license just by taking a 3-day refresher course.
All dispatcher courses in the UAE are done by Jeppesen at Emirates Aviation College as they have the monopoly and the courses are not by any means cheap either. Further, unlike the ICAO FAA certificates, the ICAO UAE GCAA license is only valid for 2 years and the renewal is expensive too.
Everybody I know in the UAE is trying like hell to get out... and there are plenty of licensed dispatcher's from the third world for employers to take full advantage of too.
Suggest you read the magazine article "The dark side of Dubai" before you go attempt something like this... unless you are of Arab descent in which you case you will fit right in. Good Luck!