Too bad you're only down there for three days. If you were staying longer, I'd highly recommend the 5 day learn to dive packages out of Cairns. You'd need to fly to Cairns from Sydney.
The 5 day course includes 3 days living aboard a dive ship and going to the Great Barrier Reef.
It's about $900/person but that's a bargain compared to what you're going to find Sydney costs. EXPENSIVE!!! You'll find it cheaper in Cairns.
A couple of links:
ProDive Diver Training - Cairns, Great Barrier Reef, Australia - Pro Dive Scuba Diving Course - Dive Training
PADI 5 Day Learn To Scuba Dive Course Cairns - Great Barrier Reef Learn To Dive - Pro Dive Cairns, North Queensland, Australia


That's a long way to fly for only three days. That's 28+ flight hours round trip from LA.