Jetstar, Qantas and Virgin are always interested in hearing from qualified dispatchers. In regards to CASA licencing requirements, there are no licences, infact Flight Dispatchers do not exist in the Australian legal framework. Having said that don't try using that excuse if something goes wrong.
The basic requirements are ATPL theory passes so a FAA dispatchers ticket will do fine.
Experience would be good.
Having said that experienced dispatchers are now rare as hens teeth, and some operators (you know who you are) are taking anybody because they can not retain staff.
As a rough guide I rate the gross income from lowest to highest as:
REX (Sydney)
Jetstar (Melbourne)
Virgin (Brisbane)
Qantas (Sydney)
Other opportunities are Universal and some of the other smaller regionals.
Having worked with dispatchers from all sorts of backgrounds, I can tell you the job varies greatly from airline to airline.