This links may provide more information
I do not work for Adobe, so I may only GUESS that a purchase in Australia must be registered in Australia, using an email and IP address in Australia
Once installed and registered, I know of no reason why a program would stop working when you move the computer to a different place
Installing to a different computer later would probably NOT work, if the email address used during activation was not the same as the original one
This MAY also be true if the IP address for the 2nd install was for a different country, so the activation server "saw" an Australian serial number but a different IP country
You will have to ask Customer support. If you are a Singapore student from a Singapore University, Adobe might require a Singapore purchase. If you are enrolled in a Australian University and get everything working in Australia, then it should later work and re-activate in Singapore if needed. But get an official response from Adobe not only over the phone, but in hard copy for future proof if needed.