Hey Brad, first thing to do is to whip over to the Roads and Maritime website and get a mooring application form, choose your preferred mooring area and then pay your application fee.
Once you have done that they'll notify you as soon as there is a vacant spot. Might take a few months or more, but unless you get on the list you could wait forever. This link will get you kicked off.
http://www.maritime.nsw.gov.au/rec_boat ... l#priorityOnce your spot is yours, the old mooring apparatus may be available to you. The Boating Service officer might help you contact the old owner. You will still need to have it serviced regardless, just to make sure it's in good order. Otherwise you will need to get a mooring contractor to sink a new one for you.
Until you get your own mooring, you're going to have to cop the $280, although Careel Bay is a little cheaper from memory and they have a tender service.
Good luck!