Unfortunately if you are sick while you are pregnant you cant call the Medcall doctors (due to insurance related issues) which I found really unhelpful. If you are really unwell you either have to wait and see your doctor the next day or go into the hospital. You can however call them out post-natal, for things such as mastitis etc.
There are only a few places that bulk bill the 18-20 week scan here on the coast, (you will need your medicare card) Life span is one, they are in located at 56 Nerang St Southport QLD 4215, phone (07) 5531 9300. Non bulk billed places can cost you up to $300.
The 12 week nuchal scans are not standard here, unless there is something wrong.
If you request a single room in the hospital after delivery it is approximately $1700 per night. Otherwise your hospital stay is covered under your medicare, and even after a c-sec you will most likely (99% chance) you will get a shared room.
In Australia they give vitamin K at birth the same as Nz, but they also give HepB, so you will be asked at one of your antenatal appointments if you are happy with this. It is an extra shot, and baby will still have another 3 HepB shots in the immunisation plan if you choose not to give the one at birth.
Once baby is born (if you fall within the right income threshold) you are eligible for the baby bonus, which is 6 months worth of fortnightly payments of approximately $380, equating to about $5000. Your family assistance will increase right away too (once you have completed the forms which the midwife will give you at the hospital)
Just because baby is born in Australia does not make it a citizen unless one of the parents hold a citizenship, so when baby gets its birth certificate (the midwife will also give you some forms to fill out for birth cert) you need to apply for 'Nz citizenship by decent' which costs around $180. You can apply for this at the same time as you apply for their passport, due to it being processed at the same place - just make sure you send the forms together. Phone the New Zealand embassy and ask for them to post you the forms.