I too will suggest you go for Binance, there are certain extent you can still make use of Binance without KYC. Also there are some other exchanges you can also use as an Australian citizen:
Swyftx (best exchange overall, quality features, low fees)
Binance (best for altcoins)
Coinspot (best local exchange)
Digital Surge (best exchange for beginners, most coins)
CoinJar (best exchange for mobile app, cash deposits)
Independent Reserve (best for SMSF investors)
Coinbase (best for debit card)
Kraken (best for trading)
Gemini (best for security)
eToro (best for social trading)
But, I will recommend you to use binance. You can even make use of p2p on Binance for ease.