Australia's health-care system outranks Canada on a range of performance indicators while characterized by a deep integration between its private and public sectors.
In 2021/22 in Australia, 41% of all recorded care episodes occurred in private hospitals. Of the total number of episodes of elective care, 58.6% occurred in private hospitals. For elective admissions involving surgery, 70.3% occurred in private hospitals.
Private hospitals are also involved in the delivery of fully publicly funded care, via contracted care or through the Department of Veterans Affairs (DVA). In 2020/21, fully publicly funded episodes of care made up 6.4% of all care in private hospitals and 2.6% of recorded care, whereas 73.5% of care paid for by the DVA occurred within private hospitals.
Because privately financed and delivered care is publicly subsidized, the extent of the public-private partnership in Australian health care can also be viewed through the lens of private hospital expenditures. In 2019/20, 32.8% of private hospital expenditures came from government sources.
Australia's health-care system demonstrates that the goals of universal coverage can be successfully balanced with a pragmatic approach that involves the private sector as a partner in the delivery of care.
https://www.fraserinstitute.org/studies/role-of-private-hospitals-in-australias-universal-health-care-system
I never used health services when I was in Queensland. But, it aint likely to be much worse than health care in Canada.