Thanks to all for your tips.
I successfully hiked to the roof of Australia yesterday, and could not have asked for a better day for it. There was not a single cloud in the sky, and the views were truly magnificent.
Plastic boots were definitely beneficial, and in fact, snowshoes would have made the whole thing much easier (I decided to bring my crampons but leave my snowshoes at home, and there was no need for crampons).
The 300 mile drive from Sydney was straightforward and took around 5 and a half hours.
Although the debate will continue as to whether Kosciuszko is truly one of the 7 summits, it does make for a very interesting trip if you ever find yourself in Eastern Australia.