I use Binance Australia although they are currently trying to...

I use Binance Australia although they are currently trying to resolve the deposit and withdrawal of AUD on their platform. Hopefully this gets resolved soon.

Another local crypto exchange is CoinSpot although their fees are very high (1% transaction fees) with a wide buy and sell spread.

You can also buy Bitcoin ETF (Code: EBTC) and Ethereum ETF (Code: EETH) via Commsec on the ASX exchange. These ETFs track the AUD value of both Bitcoin and Ethereum respectively.