You have my sympathies, I'm sure this is a stressful and difficult time for you.

I think your instinct to insist on seeing a paediatric gynaecologist is abo****ely correct. I would insist on a referral to one, preferably one that works out of a children's hospital - I think the nearest to you might be the Mater Children's Hospital in Brisbane, but I am not 100% sure. You can get some financial support through the IPTAAS service, which your GP or local Centrelink office should be able to tell you more about.

Health SA have an information page on fused labia: Parenting and Child Health - Health Topics - Fused labia

And this one from the Royal Children's Hospital, Melbourne:
Kids health info for parents

Good luck.