"Start with Irish and add a twang"?

If I'd never heard one, I don't think that would help me! Surely you have to "start with Cockney"? But even that's not very helpful.

One common trait is that Aussies "flatten out" some of their a's in ways that most others do not. In America, most people can't tell the difference between an Australian and an English accent. (Never mind New Zealand.) Where the Geico gecko is from is even raised in a TV commercial, only to be left unresolved.

You really can't describe accents accurately without extensive training in phonology. And then only other phonologists will know what you're talking about, so why bother?

Best bet: have them listen to recordings of actual Australians, of whom Steve Irwin was one.