Australian here too and it depends on a lot of things. Private hospital vaginal delivery was four nights stay post-birth and c-section is five. I loved being in the hospital personally, as I had my own room and was very comfortable!It seems like a cultural norm even if you give birth in the private maternity wings/hospitals in Britain. I remember each time the Duchess of Cambridge had a baby there was always discussion about how quickly she leaves hospital in overseas press! (I also think she just wanted to get the grim posing for the press bit over and done with )
Here in Australia I think most women stay a night and then go home if there aren't complications? But I haven't had a baby so have no first hand experience!
I believe public system they like you in for 48 hours at least if it’s your first baby and probably longer for a c-section or significant post-birth complications.