Your chief flying instructor is not being helpful. Remember, the CFI is thinking about his/her business as well...
You only need JAA in Europe. No where else. It's costly and time consuming. If you do not hold a European passport or can get a visa, then it is a complete waste of time.
If your CFI was being honest, it's the FAA licence that's recognised around the world - but don't go there!
If Asia is your main goal, the CASA licence is the one to go for. You are an Australian citizen, looking to work (initially) in Australia on Australian reg aircraft.
I (and others here) know shed loads of Aussies working in Asia that used their CASA quals to get in.
Oh and as for career objectives? They change.
Also meant to add, you don't use a JAA licence in Asia, you convert your ICAO (eg CASA) to the local one. Usually Air Law etc and the company that's hired you sorts that out.