Yes, shipping address and billing address can vary and you can have your order sent anywhere in your country (New Zealand or Australia).
When you choose New Zealand as your region, you can have your order delivered anywhere New Zealand wide.
The same applies to Australia, but make sure you change the region to Australia before you place your order in case it was New Zealand before. How? Look here: https://mybooks.zendesk.com/entries/23684627-How-can-I-change-the-Region-Language-and-Currency-settings-
Note: At this stage, you cannot have your region set to New Zealand and have your order shipped to Australia, or the other way round. Region and shipping address must be corresponding.