Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Johor Bahru to Dunedin as you normally would.
Johor Bahru Sultan Ismail Intl Airport is JHB and Dunedin Airport is DUD. These codes are created by the International Air Transport Association (IATA) and airlines use them to identify the departing and arrival airports in the flight routes they service.