Lou
March is excellent, just do Cairns on the way home. April can be fine, but daylight saving finishes at the end of March, so early golf is ok, but golf after 6pm is out (dark).
There is the Boomerang in early March, at Barnbougle....
Failing that, it depends on where you want to go and what risks you can take with good but less favourable weather.
I would suggest (if you have choices, and want to go north on the holiday) that you avoid December to March. Would you go to Florida in their summer (June-August)? If so, consider December-Feb, if not, avoid it.
Re Melbourne sand-belt, just think LA coast (not inland), and add 6 months for similar weather.
Hope to see you down under. PM me if you wish.
James B