Due to multiple factors, expect to potentially pay more when booking in January. For low rates, April can be a great choice for travel to New Zealand. Flights to New Zealand from Milwaukee in April are about $1,526 on average during April, but can be found for as low as $1,152.
Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Milwaukee to New Zealand as you normally would.