My wife and I did our honeymoon trip up the west coast of Aus with the intention of diving Ningaloo Reef from Exmouth. As a result of our experiences, my suggestion would be to go to Coral Bay, we had a great time with Ningaloo Reef Dive (
Ningaloo Reef Dive - Coral Bay, Western Australia) who actually got us out diving.
Unfortunately, the same can't be said for the dive centres in Exmouth. We spoke to a couple of them prior to our trip and were told to not worry about booking at the time of year we were going (June/July).... so we quite happily booked our flights. After the seven hour flight to Perth, and two days straight of diving to get to Exmouth... we were turned away from every dive shop because they didn't have the numbers to get a dive boat running. Of all of the centres, Exmouth Dive Centre were the most helpful - on one day they at least rented us some tanks and told us where we could do a shore dive. Bloodwood Creek was a nice shore dive, and we didn't mind the 1km swim to get out to the reef - after the disappointment of finding no other option to dive it was nice to at least see the reef.
We had two days in Exmouth, for both days we didn't find a shop willing to put on a boat for divers even if we offered to pay for extra spaces to make it profitable. The one day we did have a confirmed trip, it ended up being cancelled because the boat engine supposedly blew up. Unfortunately, that particularly dive centre didn't bother to tell us and didn't pick us up as arranged that morning - we had to go to the shop to find out what was going on.
Exmouth Dive Centre did book us on for the third day that "probably would go out", but we spoke to the guys at Ningaloo Reef Diving in Coral Bay and they guaranteed that they would be going out the next day, so we canned our trip with EDC and headed south.
If you do go to Exmouth, you will be expected to pay in full for each dive trip - which then will get refunded if/when it is cancelled. Whatever you do, PAY CASH. I made the mistake of using my credit card... thanks to day-to-day variations in the exchange rate, it ended up costing me $100 to do no diving in Exmouth.
Also, make sure that you understand that you cannot dive with the whalesharks - only snorkel, and even then I think you are expected to remain on the surface and possibly behind them not in front. Check the exact constraints before you book your flights.
Personally, I felt that divers are not really catered for in Exmouth during whaleshark season. Every time we had a dive trip cancelled, we were encouraged to book on to a whaleshark tour. I almost wonder whether dive trips were being cancelled as they were not profitable, in an attempt to shove people on to more profitable whaleshark tours or, in some cases, the Navy Pier dive. Most of the dive boats require at least four, sometimes eight people to go out. The crazy thing is that all you need to get to the reef is a small RIB that you tow across to the west side of the peninsula and shuttle out the short trip to the reef. Any of the dive shops in Exmouth could start providing this kind of service and make a killing on small group dive trips.... shuttle small groups out to the reef (two or four divers) and have a barbeque on the beach in the surface interval between dives. Overheads are virtually non-existent and they'd snap up every stray diver in town! Oh, did I say that whilst we were there that at least two other couples were also being turned away from all the shops??
In contrast to Exmouth, we had a much more productive time in Coral Bay. The dive boat went out all three days, no cancellations, no disappointments. The weather wasn't great, so we didn't get out to the outer reef but the diving on the inner reef was still very nice. There is also some great snorkelling in the bay, as the coral grows right in near the beach. The only negative comment was that on one day we were offered a "manta snorkel" between dives. You are almost guaranteed manta sightings as there is a resident population in the bay... but the reality is somewhat different than the romantic ideal. A spotter plane is used to find the mantas, then the boat DM jumps in to locate them in the water and then en-masse a group of rabid snorkellers jump in and follow it around. I felt it was verging on harassment and chose to sit it out and commented to the boat crew the reasons why. They understood, and were sympathetic - but at the same time, they have to pay the bills.
The diving at Ningaloo is great, you just have to work out a way to get to it. If the boats aren't going from Exmouth then go and hit up the shop staff in the EDC for some local knowledge of where you can at least do a shore dive.
I don't mean to sound as negative as this probably comes across, but if you are going to head to WA then you need to do it with open eyes so you aren't disappointed.