I lived in Melbourne from 1980 to around 1985.
I assisted with Scuba classes for a little while with Hatts’ Diving Headquarters. They are located next to the Melbourne Causeway.
To do any open water dives we always took our students down to West Palm Beach. According to the instructor that I was assisting, he didn’t think there was any good diving anywhere near us. And by that he meant it was all no reefs, just sandy long beach, with nothing to see.
I never actually tried diving locally, but I got the same impression for other local divers.
We actually hired a boat to take the students out for certification dives. Even do the students paid for the boat, I am sure we would have done check-out dives locally if it was suitable.
I just looked at Hatts Dive shop. It hasn’t change, but the kids are now running it. The shop looks the same as it did almost 40 years ago, with the pool on the back, etc.
I would call Hatts and ask them
http://www.hattsdiving.com/home.html
I just went to their Facebook page and all their pictures are of boat diving and it doesn't look like anywhere near Sebastian Inlet. But I would still call them.
Good luck.