I've supplied:-

Bank name
Account name
Account number
Sort Code

Is that enough for an Australian bank to send me a transfer please?

You need to give the bank accounts IBAN code. That has bank and account details in one long code.

You can usually find that on your personal account website or talk to a real person at the bank.

I know I couldn't get money sent from the US to my account, so we resorted to PayPal. That works.

Ta muchly, Bob. I've provided the IBAN (International Banking??) code.
I hate paypal and am currently in dispute with them