Wiki created with links to AU & NZ government web sites. Use at your own risk. They may not be up to date.

For Australia a separate permission to cross a state/territory border may be needed (NZ to state-territory and/or state-territory to state-territory).
What is in effect any at a time can be hard to determine. Some states (e.g. WA QLD) have changed the requirements at short notice in the past.