Your licence needs to match the aircraft registration. Which is a subtly different that requiring a licence for the country. There are quite a few Aussie pilots working in Asia on Australian licences flying VH registered aircraft.
In order to have a licence issued by another country based on your Australian licence, you need an email from CASA to the other authority confirming your Australian licence.
CASA will not do this for the old CAR 5 licences, only Part 61 licences. I found this out when I got my last Thai licence renewal. CASA put me on the "fast track" to issue a new Part 61 licence. They promised 10 days. It took 3 months. If you are thinking about an overseas licence, get your Part 61 licence in order - now.
All the the I was waiting for CASA, a very nice Thai was emailing CASA asking when they would be able to confirm my Australian licence. She copied me on the emails and the CASA responses were farcical. There was one person at the Thai DCA handling my licence, but in Australia we could never speak to the same person twice and no two people ever gave the same advice.
The other small trap is that CASA charge $75 to confirm that you have a licence to an overseas authority - but they don't tell you. If you don't pay this fee, simply nothing happens. But its the overseas authority that requests it - not you. So you never make any application that would alert you to the fact. You are just supposed to know. So, as soon as you apply for an overseas licence, you must go to CASA and get the payment form to release details to a third party and pay the fee.
I have dealt with the US FAA. The NZ CAA and the Thai DCA. CASA is the worst to deal with. The Thai DCA makes us look like the one that is a third world country.