As in Europe and North America, most mainstream credit and debit cards are accepted everywhere - though not for small transactions. You should consider making international transactions through a broker.
ATMs are widespread in Australia, though bear in mind that many machines charge a fee if you’re not with their bank (this shouldn’t be more than around AUS$2).
If you have a credit card, or decide to get one, Visa and Mastercard are universally accepted. Even so, always carry some cash as many shops won’t accept card payments for anything under AUS$15.
If you need to transfer money within Australia, your bank will almost certainly have an online facility for this, or you can do it in-branch. If you need to transfer funds back home, consider an international broker like HiFX or Caxton.