The bird of the month for June is the Grey Fantail (Rhipidura albiscapa).
This small songbird is common all over Australia and frequents a wide range of habitats from forests, coastal scrublands to swamps and urban backyards. They are quite distinctive in flight, flitting between branches as they catch small insects on the wing, fanning their impressive tail as they fly.
In Stanwell Park, where I spotted this one, I often see them about after rainfall as they take advantage of the increase in insect activity. I got this photo in my front yard as the bird briefly perched between feeding bouts in the light drizzle.