Will they let me fly?
 

I'm an Israeli holding an American passport. I want to do AKL - MEL on EK. Their price on this leg is very cheap (about 175 USD with free date changes). Should I excepct trouble with the airline?

I do not think that you will have problems at all.

The UAE and specialy the emirate of Dubai are not conservativ like may be other arab countries.

Emirates is a multi culture airline which like to expand into the american market.

Not an issue
 

You will have no trouble at all. I fly that leg regularly with business colleagues who hold Israeli passports and there is never a problem. UAE (read EK) does have strict enforced rules about valid visas however if you are travelling on.

Is that USD175 one-way or return? If one-way then you can do much, much better buying from NZ websites.

Not taxes on trans-tasman flights are quite steep, and NZ departure tax wont be included - NZD $25 must be paid at the airport.

I need a ticket out of NZ before I get there because I cannot enter on a one-way ticket (my return is from Sydney). The final flight date is not set yet and will probably be determined at the last day or 2. The EK price is ~NZD250 - fixed coach price with no fee for date change and almost guaranteed availability. The AirNZ price is NZD129 with NZD100 penalty for changes plus fare difference. This is why I like the EK deal better.