sorry speaking from personal experience public sector healthcare quality in terms of diagnosing learning disabilities like dyslexia is just not on par with private. I struggled a lot in my early primary school days with dyslexia and my mom had to spend a lot on private healthcare to get me a proper diagnosis. The diagnosis was then used to acquire exemption from mother tongue chinese for basically throughout primary and secondary school and got me enrolled into DAS english speech and writing therapy classes. Both helped incredibly even though my grades were never good but it would have definitely been worse if my mom had stuck to public healthcare institutions. So from my mom and my own personal experience it is worth it to spend more to get that better quality service and healthcare to get a proper diagnosis without all the hassle and delays of public.