I fish in Australia a couple of times a year, always in the 'Deep North' of Northern Territories, Queensland and Western Australia. The fishing is best at the end of the tropical rainy season in April. However, the wet season can run long or finish early, materially affecting the fishing. The safer time to visit is Sept-mid-November in the build up to the Wet. The air and water are warming up and the fish go on the chew. The later in the year, the better the fishing subject to (a) really really HOT weather and (b) the possibility that the Wet starts early, which complicates matters.
June-August is winter in Australia. There's still good fishing up north, but it's not as good and some operators shut down or go only part-time. If you're going to be based in Sydney or Melbourne, then that's a whole 'nuther topic altogether. I've not fished down that way but there IS winter fishing to be done, both fresh and salt.
I'd check out
www.fishnet.com.au. It's the best site I've found for Australia fishing and has a bulletin board where you can ask specific questions.
If you want the names of some excellent guides operating out of the Darwin area, send me an email and I'll put you in touch.