I called the SA Firearms branch this morning to enquire about doing some hunting in S.A early next year. Spoke to Jan who was most helpful and answered all my questions and offered some good advice.
Apparently so long as I apply for a hunting permit online I can vaporise any number of feral's on private property with any calibre I see fit to use. I'm even allowed to bring my big guns into the state and use them so now I'll get serious about planning a trip to my uncles "Hobby Farm". When I say hobby farm, it's 20,000 acres with access to another 30,000 acres next door.
She did mention that in relation to 50BMG / 416 / 338 & 375 Chey that I'm fine to bring them into the state but I cannot allow them to be stored with my uncles firearms as he's not technically licensed for them.
Also in relation to shooting them I need to ensure the likelihood of the projectile leaving the bounds of the property was considered which won't be an issue on 20,000+ acres. Also, apparently they don't restrict the ownership of these calibre's but they do restrict their purchase and possession. The hunting permit seems easy enough to apply for so I'll get that sorted in the next few days.
They have a list of feral animals that can be hunted which is mainly goats, pigs, deer, rabbits & foxes. No mention of camels in that list but I did find camels listed elsewhere as being feral so I'll need to clarify that as one of the main ferals on the farm are camels.
http://www.environment.sa.gov.au/managing-natural-resources/plants-and-animals/Permits_licences/Native_animals_in_the_wild/Hunting_Permits