Whirly,
If I could just add the following, OZ is a bloody big country compared to the UK and subject to different weather zones. The top1/3 of the country is monsoonal which means very poor flying conditions in the summer months. (Dec to March ) with low cloud not much better than tree top level for days on end. Cairns is in this region and with moutains all around it except out to sea and the airport being a controlled one means you are likely to be going nowhere VFR. June to Sept is the opposite in that region, blue sky's and little wind, and is the tourist season up north with plenty of eye candy on the beaches.
Southern parts (Sydney, Melb, Adelaide etc) have more traditional seasons like the UK only at opposite times to the nth hemisphere ofcourse. Summer can be very hot 42'C with lots of thermal turbalance and winter like the UK, fogs, rain etc though no where near as often.
In my opinion if you want to fly here and have a limited time to fit it all in so do not want to be grounded due to weather,the best time is late March till early May. This will give you the best average weather all over the country and is traditionally the best time of year to fly in the south. Start your holidays down Sydney way if that is your chosen place and move up to Cairns last before going home.
Hope that is helpfull and enjoy our weather and scenery.