Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Portland to Dunedin as you normally would.
In terms of precipitation, rainfall in Dunedin ranges from 2.4 - 3.1 inches per month. January is typically the wettest month, when rainfall can reach 3.1 in. September is typically the driest time to visit Dunedin when rainfall is around 2.4 in.
If weather is an important factor for your trip to Dunedin, use this chart to help with planning. For those seeking warmer temperatures, January is the ideal time of year to visit, when temperatures reach an average of 57.2 F. Travelers looking to avoid the cold should look outside of July, when temperatures are typically at their lowest (around 41.0 F).