Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kentucky to New Zealand as you normally would.
Due to multiple factors, expect to potentially pay more when booking in May. For low rates, September can be a great choice for travel to New Zealand. Flights to New Zealand from Kentucky in September are about $1,524 on average during September, but can be found for as low as $1,274.