So Aussies and Kiwis can live/work in the other country without visas (instant residence) but whoever drafted that agreement really fucked up. Aussies get instant ACC in NZ but Kiwis don't get Medicare in Australia. I remember there were discussions about it on Radio NZ a few years back.
There is a big private health care industry in Australia (for better or worse) that's not employer based (you see adverts on TV), so I'm guessing a lot of Kiwis just get private care in the AU.
But I'm wondering how much it costs an actual Australian resident/citizen with medicare. I know as a non-resident, a doctor cost around $70 ~ $80 (went once in Melbourne and once in Sydney) and I saw a real doctor. That's a far cry from America where you pay $200+ to see a Nurse Practitioner (yes, pretty advanced, but still not an MD).