OzForex? CurrenciesDirect? There are many similar exchange agents: You transfer to their bank account of country 1, they transfer from their local bank account in country 2, avoiding international transfer fees. Few days, less than 1% away from the Google rate, unbeatable.

Australia and NZ have different currencies so there is no way you can avoid dealing with the money changers. There was a bit of debate a few years back about if Australia and NZ should form a single currency, but it did not seem to get far.

https://transferwise.com/u/0aa62 will do it for $5ish. That's my referral link.

Edit: BankWest in Australia has a no-conversion-fee Mastercard.

Depends how much you want to move :)

I used Tranferz a few times when I moved from Aus to the US. Free for over $5000 last time I checked.

http://www.tranzfers.com/Referral/matthodge