Depends on the state, but in principle yes. And tertiary education involves fees nationwide.
STNI and ENS are permanent. However both require some work experience LA can be either temporary or permanent, however not many people get LA visas.
Don't forget:
- Skill Matching, permanent visa, similar to STNI, but you only need 6 months send work experience in the 12 months before application, this is less than STNI.
- RSMS. Also a permanent visa, no work experience required, however RSMS does carry a legal obligation to make a "genuine effort" to work for your sponsoring employer for 2 years. Your visa can be cancelled if you don't.
The one to beware of is the subclbutt 457 visa, temporary visa (work permit), lots of people have hbuttles with this. You may also hear about SIR - Send Independent Regional - again, as a nurse forget it, you ought to be able to get a better visa than that from the list above.
Check the booklets for details, migration booklet 5 for ENS, RSMS and (permanent) LA, booklet 6 for Skill Matching and STNI.
-- This is not intended to be legal or professional advice in any jurisdiction