As a New Zealand citizen do I have the right to study in Australian University?
You may apply for a student visa, which is granted by the Australian Department of Immigration and Citizenship (DIAC). DIAC will only grant student visas for registered courses (those offered by Auestralian education providers registered with the Australian Government to offer courses to overseas students).
You must have a student visa if you intend to study for more than three months.
Once you receive a letter of offer or electronic Confirmation of Enrollment for your full time course of study, you can apply for your student visa. Visit your local Australian Government Office to get more information on applying and which documents you need to attach to your application.
Visit http://www.immi.gov.au/students/ for more information.