health insurance?

Kia ora, I'm just another kiwi that will be crossing the ditch to move to Australia in September (NSW). I was diagnosed with endo a few years back and currently have an IUD to help with my pain. I am curious whether private health insurance would be a good thing to have, or if Medicare would suffice. Just for things like IUD renewals and gyno consults. They can be expensive here in NZ if you go through a specialist without insurance. What do you guys recommend?