Great to hear you'll be moving here, most of us are up North but a fair few are down south. Where abouts are you planning on living Stefano?
Adelaide rego (in my experience) has been an absolute breeze, pay for the inspection + permit, take the car down there and they have good look at it. My last one didn't go through a brake test, he just popped the bonnet and shone the torch around the engine bay and that was that. Your ute is tidy so I think if you bring it in there looking stock (12 inch wheels etc) you should be fine.