Coinbase offers credit or debit card purchases for Australian traders for a fee of 3.99%. You would be required to make USD purchases and after the full verification of your account, which includes email, phone, ID and proof of residence.
Exchange bitcoin with Coinbase
Pros
provides high purchase limits;
instant access to BTC through credit/debit cards.
Cons
the exchange is known for tracking its user’s activities;
full verification needed prior to bitcoin purchasing.