She is only 8 yrs old, she has time to catch up, but it is good that you are acting now to seek assistance for her.
If she is at a State school, surely they would have resources to refer her to appropriate assistance?
Also check at Centrelink, see if they can advise you.
The school has ongoing speech resources but have recommended if possible to speed up the process by getting a private diagnosis to provide access to them. Her teacher and I both have over 60 years combined experience in working with children and we can't put our finger on the exact problem as she doesn't quite fit dyslexia or ASD etc but something is impending her learning. She can read but not spell properly nor seem to retain spelling words and she has trouble writing. When asked she gives a couple of sentences but no more.
Hoping for better luck tomorrow with call back from one specialist.
Privately,often the really good peads are full like you say, and won't see new patients.
Maybe you could try googling peads all over Brisbane and ring them and see who may have the earliest appointment.
The fee is substantial ( $300 ) but most of that is medicare funded. If you are seriously struggling, theres no shame in approaching a charity for help like Salvation Army.. Let us know how you get on.