Someone at Airservices will book a DAME visit for you, but you'll have to book the eye specialist appointment yourself. The main problem is CASA. They're basically stuck in the 60s as far as public service efficiency is concerned.
Don't worry too much if you can't get it all done in time. The next enroute course starts in Melbourne in September, you can just relocate down here if they recourse you
It's not as bad a people make out, honest