Hmmm, it's likely that your device is running an iOS version lower than iOS 6. You can check which software version you are running by going to "Settings > General > About > Version". Advice on upgrading your software version can be found here.
It's also possible that you're signed in to the iTunes App Store with an overseas Apple ID. Make sure you sign in with your NZ account as the app is only available to folks based in New Zealand!
To check, tap Settings > iTunes & App Stores > Apple ID, View Apple ID > Country Region
You can either change the country/region of your current account without losing any of the content you have purchased from Apple - or you can sign out and create a new account that is registered in NZ - and then sign into this account in the iTunes store to download the app.
Once you have downloaded the app, you can sign back into your overseas account. You'll just have to log in and out of the stores when you are notified about any app updates - which isn't too often.