You can currently apply and start the CA Program in Australia and New Zealand, and continue your subjects in any of these two countries if you move there. You will however, be required to meet the approved employment requirements in whichever country you move to.
If you change country before completing the Tax and Advanced Tax subjects, you should take into account that this subject will be different in Australia and New Zealand. In this case, you will be responsible for ensuring that you have the necessary knowledge for each subject.