This moth rested on my verandah for a day. It turns out to be a female Crexa Moth, Genduara punctigera (thanks to Dave Wolfe for the identification).
Crexa Moth larvae feed exclusively on the semi-parasitic tree Native Cherry, Exocarpos cupressiformis (also known as Cherry Ballart). Native Cherries are common in bushland around Newstead, and the nearest natural stand to my place would be about 1km further up Palmerston Street.
My many attempts to propagate Native Cherry over the decades have only resulted in ONE specimen, which I planted next to the Yellow Gum at my gate so that it can tap into the root system of that big tree for nutrients and water. I will be so delighted if this or any other female Crexa Moth decides to lay eggs on my Native Cherry and I get to watch the whole life cycle!