To find out requirements for becoming registered as an RN in Australia you need to check with the appropriate state Nursing Board.
For example in Tasmania;
OVERSEAS NURSE APPLICANTS
♦ Overseas nurse applicants who undertook their education preparation in United
Kingdom, Ireland, South Africa (and who gained initial registration/enrolment with the
South African Nursing Council), New Zealand, United States of America, Canada and
Singapore may apply direct to the Nursing Board of Tasmania.
♦ Overseas nurse applicants coming to Australia from overseas countries (other than
those listed above) may apply direct to the Nursing Board of Tasmania for assessment
of their nursing qualifications.
♦ Overseas nurse applicants who are applying for migration should first contact the
Australian Nursing & Midwifery Council for an application form for assessment of their
nursing qualifications prior to making application with this Board. The address is
www.anmc.org.au
In NSW;
An English language test is frequently not required where an applicant's nursing course was completed and the person subsequently registered as a nurse in Australia, New Zealand, United Kingdom, Ireland, the United States or certain parts of Canada.
I noted in all cases an IELTS score of 7.0 is required if your initial training was not done in English.
The Boards of Nursing are your first port of call for any questions on Australian registration.