On your phone, replace the leading 0 on all your NZ contact numbers with +64. That is the correct dialing format for mobile calls/sms from Aus > NZ. And your number, (when they sms back, etc), they should dial +61 (again, instead of the leading 0).
Also, how do I call NZ from Australia?
For calls to New Zealand from Australia dial: 0011 + 64 + area code + telephone number. For calls from New Zealand to Australia dial: 00 + 61 + area code + telephone number. For further information (eg. area codes) please visit the White Pages - international dialling codes.
How many digits are in a New Zealand mobile number?
Landlines. New Zealand landline phone numbers have a total of eight digits excluding the leading 0: a one-digit area code, and a seven-digit phone number (e.g. 09 700 1234), beginning with a digit between 2 and 9 (but excluding 900, 911, and 999 due to misdial guards).
How do I call a mobile number in Australia?