Undersea Explorer, and Taka are quality outfits and should be what you are looking for.
Mike Ball is great, but too expensive unless you are flexible on dates and can get Standby rates.
Australia is absolutely wonderful and the people are very nice.
The Great Barrier reef is very nice, but if you can get out further into the Coral Sea, the clarity and sealife are nicer. Try to get to Flinders Reef, Holmes Reef, or Bougainville reef in the Coral Sea as this is where the better diving is. Forget Cod Hole, fish feeding is a waste of one dive in my eyes.
Avoid the Aquarius out of Cairns. It was cheap but completely incompetent and borderline unsafe. I booked just 1 hour before the trip departed and they claimed they had serious intentions to get to Holmes and Bougainville Reef depending on the weather. 1 hour after on board the claimed they couldn't make it because of rough seas. Since the boat was half full and the weather was excellent it appeared more likely they wanted to save on fuel costs. I felt they lied to me to get my business. There were several accidents that occured and crew that condoned taking lobsters and fish in forbidden zones which didn't go over well with me.
GO STANDBY AND SAVE OVER HALF
Aussies gouge Americans and Japanese on prices when they book ahead of time. That is why you won't find prices on Mike Ball's website or why operators want to know where you are from prior to quoting prices.
I went backpacking style in Australia for 2 months carrying my gear around. During that time I did 3 week long liveaboards each was done without prior booking on suggestion by a friend. The "standby" rates were less than half of what they charge Americans who pre-book by internet. If you can go in the April-May time frame before the tourist season, there are many live aboards with available space.
I did Mike Ball's Townsville - Yongala and Coral Sea trip for $1696.00 Aussie Dollars (under $900 USD) and they normally charge USD $2400.00. It was by far the best, it takes you out past the GBR where the water is clearer and the sealife more abundant. It was far superior to his PNG trip and we had spectaular weather for diving the Wreck of the Yongala (in the Top 10 wrecks in Rodales)
Here is a scan of their brochure that you will only find in Cairns. It looks the same as the worldwide brochure, but has extra, black overprint boxes at the top with the prices in Aussie dollars. They'll probably kill me for showing it here.
Mike Ball brochure with Standby Rates found only in Cairns *Click Here*
*Click here* to see 23 photos from The Great Barrier Reef Trip
*Click here* to see 22 photos from The Coral Sea and Wreck of The Yongala trip