As an accountant who has experienced this many times I prefer cleints maintain a spreadsheet summary of rental income and expenses that is continuously maintained in NZD !!!. It makes the basis for a way to cover the different tax periods and convert the NZD into AUD using the relevant rate. (usually ATO monthly average rate)
Also give your AUS agent copies of the NZ return and assessment ntc as the tax paid (if any) may be a credit in your AUS return.
NOTE : You DONT include the rental income in a rental schedule in Australia. You report it as foreign income. That way any NZ tax is credited. This avoids dual taxation.
Its a common and simple issue really. There are many issues that can be messed up.