What is the best way to convert Australian dollars to New Zealand dollars at a very good rate with no fees?

It's impossible to convert currency without any fees, as all services offering currency conversion will charge something for their service. You should check out Currency Online though http://bit.ly/o5cqUq, as they charge a very small TT fee of $9 and their commissions are much lower than banks - so the rate is significantly better! We use them all the time still to bring money to Australia.