Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from California to Cairns as you normally would.
Due to multiple factors, expect to potentially pay more when booking in March. For low rates, July can be a great choice for travel to Cairns. Flights to Cairns from California in July are about $1,517 on average during July, but can be found for as low as $986.