For all Australian residents it can be done free (via Medicare), or by choice it can be done privately via Private Health Insurance cover. I think that is correct anyway as that is how our system works for most surgery. Most surgeons will do public and private work so the standard is the same.
But if you are from overseas and need/want to come here for surgery that would be a different matter. You would need to enquire from your surgeon of choice and hospital as to all out of pocket expenses. This would include anaesthetist, hospital stay, blood tests and surgeons costs etc. It would be expensive but maybe they could do a deal.
I'm sure someone here is more qualified to answer your question than I am, as I do not have a child with CAH - although I do have CAH myself.
Le, I think you said at one stage that you are living in Vietnam - a thousand apologies if I am incorrect, but if so, here are a couple of suggestions. Have you contacted Kate Hansen as she is both an Australian doctor, as well as, the founder of CLAN which takes visiting CAH medical teams to Vietnam and Philippines? She may have some ideas she can suggest. Also Professor Garry Warne has a great interest in both CAH and Vietnam and has lead many medical teams there over the past 18 - 20 years. He may also be able to offer you some suggestions.
I can give you their contact details if this is information that you have not already investigated. Just email me on: mrjgreen (at) bigpond.net.au - replace the at with @ and delete the spaces.