I have used CoinJar and Local Bitcoins. I mostly used local bitcoins these days, because there are a variety of sellers, so sales can be spread among them so I am not hitting a withdrawal limit of an exchange.
I would be interested in other opinions of Australian exchanges, especially for buying. (I actually did most of my buying back in the day with a German bank account from when I lived there and did some freelance work for a company there.) Market prices in AUD seem to be slightly higher than you get by converting the USD price into AUD, so perhaps we have more buying demand here than elsewhere.
FYI: https://www.buybitcoinworldwide.com/australia/