If you are talking about non urgent procedures then QM has an excellent reputation, but things do move slowly compared to going private. Think three months for first consult, another month for the second, another month or so for MRI, etc etc. Private you will be in the OR in a week or so.
@rani has suggested three top surgeons who not only are professionally but ethically competent, unlike one group mentioned before on this site (Clue-motorbike) who will have you in the OR with indecent haste.
The downside of @rani's suggestions is they are private, as far as I know, and they are general surgeons. I feel that for something as complex, and potentially devastating if mistakes are made, that a specialist spine surgeon should be seen.
The cost of going private can be eye-wateringly expensive. My ten hour session in the OR, Adventist Hospital, not more expensive Matilda, was $300,000, just for the OR, not the extras which were around $50/-. Add in $100/- for surgeon, $50/- anesthetist, the bill adds up, fast. Insurance rarely covers the OR costs, BUPA caps that at $30,000 per operation for example.
If you need any info on this, plse ask.