Hi Nikki,
From your location, I gather that you are on a long stint travel - either round the world or a backpack trip? Australia will be a fun leg.
You didn't mention your budget but trips in the GBR can vary in price depending on the lengths, type of boat and the level of luxury. I remember doing one travel stint from Thailand to Australia and had a money shock upon arriving in Cairns.
Having some industry experience in that part of the world, the one thing I would say to experienced divers is to avoid the boats that take Open Water courses on liveaboards. The dive schedules are all taylored to the student dives and the "real" divers can end up being a bit of an afterthought.
The central hub for trips to the GBR is Cairns. There are many companies that do trips. My opinion is that you really have to get out into the outer Barrier Reef or up North into the Coral Sea to get the best in marine life and the way to do this is on a longer liveaboard.
I've taken a trip with Taka (
TAKA DIVE - Scuba diving and Liveaboard dive trips to Great Barrier Reef). They didn't do OW courses - just certified divers - and covered the highlights. I don't know if they still do but they had standby rates at certain times of the season and it was quite a bit cheaper than the regular rates.
But if you get a chance, also consider doing the Yongala out of Townsville. It's a brilliant dive.
I think Australia - especially the traveller's routes - are really good for solo women travellers. There are many options and on-land attractions. Just watch out for bedbugs in some of those lower-end guesthouses :shocked2:.
Happy travels