I have been through the process already converting JAR-CASA, where are your family based in Aus?
Its pretty clear on the CASA website what you need to do, from memory it all started with a Medical, which led to an ARN, which led to an ASIC, then 3 exams (CPL & ATPL Air Law, and IREX), then you will need to find a flying school to do the conversion. I can strongly recommend AD-ASTRAL aviation, based at YPPH, having tried to do it through el-cheapo flying school at YPJT who had no idea what they were doing, I switched to AD-ASTRAL and they were just superb.
The whole process costs quite a bit, I would strongly recommend buying the books and getting stuck into the study for the exams as early as possible.
Good luck with it all...