Due to multiple factors, expect to potentially pay more when booking in November. For low rates, September can be a great choice for travel to Auckland. Flights to Auckland from Kaua'i in September are about $1,028 on average during September, but can be found for as low as $674.
Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kaua'i to Auckland as you normally would.