Tourists are able to open a bank account in Australia. They just need their passport and a valid visa as well as a few address/contact details. Tourists can even apply for an account before they arrive in Australia.
While a tourist visa might imply a short stay, it is generally possible to open a bank account. The easiest way is often to start the process online with a major bank before you travel, and then complete it in person with your passport shortly after you arrive in Australia.