You would need a referral to see one. They may charge up $100 I wouldn't think any more than $200 for the initial consult. You would also get a rebate from Medicare. You can get the initial consultation item number from the Opthalmologist and then look up MBS online to check the Medicare rebate. The Optometrist can write the referral.
If you go to an Optom, they are would not prescribe glasses if she didn't need them, they may even do both, glasses and patch depending on the severity of the lazy eye.
Ask the Optom if he knows what the local Opthal charges.
Just one thing you may need to think about, it would be worth looking into PHI for DD just in case she needs the turn operated on for correction and check that she would be covered for the operation, as in incase they turn around and say it is a pre existing condition and would not be covered. You can go public and be on the wait list if PHI is too much.