A friend had a quote to get it done privately as she did not have PHI either. She was quoted $4000 there abouts.
Another GF had her grandson done publicly and as he was put as a high category he was operated on very quickly. So check with your GP on the category system and the public hospital for waiting times.
She has noticed a huge improvement in all aspects of sleeping ans speech. She also said while they were on the waiting list it was nerve racking but OK as they knew it would be Ok in the end.