We flew a 58 Baron from the Gold Coast-Lord Howe-Auckland. Apart from a bursting bladder (mine) it was little problem.
Arrange to clear Australian Customs in Lord Howe. The local, and only policeman, was also the customs agent. Check your ERSA for details who to contact.
You will need HF, life vests, raft, etc.
Arrange an arrival time to clear customs in Auckland before departing Australia.
If flying a single with no ferry tanks I guess you would want to go Port Macquarie-Lord Howe-Norfolk-New Zealand. However someone more familiar with a single-engine crossing would know more than me.
Good luck.