Hey Sambo,
IN Sydney at that time of year you'll need everything you got. I'd bring a 16 or 18, a 12 or 14, and a 9 or 10 as well as two boards one for light and one for strong winds.
That time of year you can expect some decent Southerlies around 30 knots and the odd Nor Easter at around 15 knots, but mostly Sou' Wester and the tail end of the winter westerlies, very gusty.
Dont know much about the Cook Isles, I'm sure someone has been.
Good winds