Private V Public Hospital Etc. - Australia

Stacey
Hi ladies. Just wondering if any Australian ladies have any experience or have done any research in relation to private v public doctors/hospitals etc. for pregnancy and birth. 
I currently have very minimal private health cover and if I increase it i think there is a 12 month waiting period anyway. I'm TTC as soon as possible so probably not worth increasing.
I've had some friends go public and it all seemed fine. I'm not telling anyone I'm TTC so don't want to ask them any questions at this stage! 
Am I right that pretty much all costs are covered under the public system??