It is highly unlikely that your 'NZ Trust' is not a resident of Australia and as such would likely be taxable in Australia.
The residency tests under Australian Tax Law looks to the real management and control of entities, which is essentially the controlling mind not where the trustee is incorpororated and not just who are the directors on paper. Refer to the Bywater case in relation to this.
Now even if you manage to structure in a manner where said trust is not a resident (something that your local accountant is very unlikely to be able to succeed in) you still have the transferor trust rules, which essentially mean that if you have provided the funds to the trust then you will be taxed on the income of the trust that would have been taxable were it a resident of Aus.
If you then manage to get passed the transferor trust rules you then have to contend with s 99B of the 1936 act, which means you would essentially be taxed on any amounts received from the trust.
In conclusion, whilst it is possible to do what you are saying it is far from easy to do so and the legal fees to adequately setup the structure usually go well in to the 10s of thausands. Furthermore, whislt you may be 'getting away' with not paying tax I think it is highly probable that your trust would actually be taxable in Australia in which case I wouldn't be bragging about on a public forum nor would I be advising people with very little knowledge on tax affairs to follow your example.
