New Zealand citizens do not need a Student Visa to study at a tertiary level in Australia. As a New Zealand citizen studying at an Australian university or other tertiary institution, you are also entitled to pay domestic student fees, instead of international student fees, which tend to be higher.
However, you will not be entitled to student loans, allowances or able to participate in the FEE-HELP or HECS programs. You will need to pay your fees as a full-fee paying student every semester or year, depending on the institution you are enroled in. Fees and conditions vary between institutions, so check with the institution for costs and key enrolment and payment dates.
If you are a temporary or permanent resident, and not a citizen, of New Zealand, you will need to obtain a visa to visit Australia. For more information, contact the Australian embassy or consulate or visit the Australian High Commission website.