As far as converting your future Oz licence is concerned you will have a CPL and nothing more. Although it's a convenient short hand, fATPL doesn't exist although in Europe it's usually taken to mean CPL & IR issued + ATPL exams completed. Foreign authorities only recognise the licence you hold in your hand, not some potential future issuance.
Your question has been asked a number of times on PPRuNe. Use the search function & you should find the info. you're after.
The short answer is that you will need to meet FAA minimum experience requirements for the licences ('certificate' in US terminology) you seek eg CPL or ATPL, pass the relevent theory exam for those certificates (single exam per certificate, including IR), pass at least a Cl.2 medical (CPL & higher certificates) and finally pass a flight test for the issue of each certificate.
Note that FAA min. experience requirements are often different to Oz or JAR-la-la land specifications.