Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from North Carolina to Canberra as you normally would.
In terms of precipitation, rainfall in Canberra ranges from 1.2 - 2.4 inches per month. October is typically the wettest month, when rainfall can reach 2.4 in. June is typically the driest time to visit Canberra when rainfall is around 1.2 in.
If weather is an important factor for your trip to Canberra, 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 68.0 F. Travelers looking to avoid the cold should look outside of July, when temperatures are typically at their lowest (around 41.0 F).