Good morning Sukhoi.
This an old ad but it might give you an idea what Jetstar are looking for. As far as I know they are the only ones located in Melbourne. Qantas dispatch are located in Sydney and Virgin dispatch are located in Brisbane. The prerequisites for Virgin are similar to Jetstar and depending on your experience a degree is not mandatory.
Good luck in your search as being a flight dispatcher is a good job.
Cheers Hoss58
Dispatch Operations Officer - Jetstar | Melbourne VIC (simplyhired.com.au)