Great Barrier Reef

It's been a few years but we organized our trip with Quicksilver: 20-25 minute helo flight out to Agincourt Reef, where we were met by their dive boat for a Scuba excursion that lasted about an hour, then a boat ride over to the larger vessel that everyone else came out on that morning. Spent the rest of the afternoon snorkeling and lazing about the ship before the ride back to Port Douglas. Wasn't cheap, but it was extremely well organized and, in our opinion anyway, was worth every penny for the once in a lifetime experience.

For a "dive" -- do you have SCUBA certification? Snorkeling not a problem, but SCUBA certification takes more time than you have.

We do have one person certified to dive and he would like to do so. Again trying to avoid the crowds if at all possible.

I wouldn't worry too much about the crowds on the boat. Once they arrive at the reef they disgorge everyone onto a huge floating platform where there are a variety of activities to keep everyone occupied - there's plenty of room.
On the ride back to Port Douglas we were so comprehensively bushed that we slept the whole way.

Maybe have a look at this one.
http://www.seastarcruises.com.au
Not sure how you can work in a fly over as well.

A few points, based on personal experience:

• from what I understand, after you dive, you need to be on the ground for a full 24 hours before you can fly (I don't know if this includes helicopter flights or only commercial flights; also, I don't know if this is just something you need to sign as a waiver or whether they can enforce it)

• we used Compass Cruises when we were there a couple of weeks ago, but the seas were very rough. They offered the option of switching to a different day. As we were there just for the day, we didn't really have an option. Got badly seasick and was unable to participate in the snorkelling (which is all I had planned) - should have gotten the preventive medication. I don't understand the point about floating platform. Where we went, it was open ocean as far as I could see. I don't think there was land anywhere close (else I probably would have wanted off the boat!!). But we likely went to the outer reefs, as the journey was about 2 hours or so each way.

• if you want a recommendation for a place to stay, I vote for Steve's Grand Barron Lodge (airbnb) in Kuranda. Steve is an expat and really takes good care of his visitors.

Porcupyn

Note: Flying (well, altitude) after diving can cripple or KILL you. If you are a certified diver, you're supposed to know this. "The bends" is serious and not to be taken lightly.

That said, the "24-hours between diving and flying" guideline is a generally adequate and usually gives you plenty of margin for safety - it's easy and almost always keeps you safe. But you need to factor in how much diving you have been doing to what depth (the effects are cumulative). If you're just doing one or two casual dives in a day, you'll be fine to fly if you wait 24 hours after you get out of the water. Note that it's not only flying you need to watch after diving - if you finish diving, jump in a car, and head over some mountains you can get in trouble, too. Conversely, flying less than 24 hours after diving CAN be safe - if the plane flys very low (I'm not kidding - I was on a week-long dive trip on the GBR and some divers left from a small island half-way through the week and flew back to the mainland, on a plane that stayed v-e-r-y low). This was a flight specifically for divers so they know about the requirements. Ultimately, it's your responsibility to know what you need to do to stay safe - don't count on anyone else.

Stepping back from the "avoid getting bent" advice, about the GBR: if all you can possibly manage is a day trip, then Cairns may be your best option. But like so many popular places in the world, tourism (in this case, dive tourism) has been loving the GBR to death. Cairns is definitely a mass tourism destination, so don't expect to find places without other tourists. And the impact of tens of thousands of day trippers (along with a bunch of other factors) has taken its toll on the reef environment right around Cairns. Locals joke that they now call it "the Pretty Good Barrier Reef" (that is, not as great as it used to be). If you can get a bit further out, you will see much more of what you have been hoping for. For that, you probably need more than a day. I figure it's worth it if you can find a way (unless you expect to visit Australia frequently). We loved our trip to the outer reefs. Osprey Reef was awesome - friendly, curious, playful potato cod the size of a refrigerator, oodles of sharks, and all kinds of other things. At night the ocean seeming to "boil" with fish...so much life... Highly recommend a live-aboard if you can manage it. Have fun, good luck, and be safe!

For Porcupyn: "I don't understand the point about floating platform. Where we went, it was open ocean as far as I could see."
Quicksilver apparently has exclusive mooring rights at their platform at Agincourt Reef. Can see it in their website photos. The combination of their large catamarans and the stable, anchored platform once you get there makes for a much more comfortable experience for those prone to motion sickness. The tradeoff is that the larger vessel is not a particularly intimate experience - they move a lot more people than the smaller boats, which will rock and roll a lot more if conditions are rough.
That link to Seastar cruises looks like a pretty good small boat alternative to Quicksilver.
For OP Donna - I noticed on the Quicksilver website that they offer a 10 min helo ride upon arrival at the reef, as well as some Scuba options for both certified and novice divers. Didn't see the "Fly out, ride back" option that we did so have to assume it isn't offered anymore, though it's probably worth checking with them directly if there's interest in such a thing.
Good safety reminder about diving and flying. The Quicksilver dives were rather shallow as I recall (30-40 ft) but you'd still need to factor in a no-fly day after completion of the dives. The helo rides never exceed 500 ft, FYI.

We did the same type of tour Robert did with Quicksilver to Agincourt Reef. Quicksilver does offer short helicopter rides over the reef (short and not cheap, but great views) as well as options to snorkel, scuba and helmet dive. While it was a fun day and Quicksilver runs a good operation, it was incredibly crowded with hundreds of other passengers on the boat.

We had a far better time when we snorkeled off the Low Isles which are only about 15km off shore from Port Douglas, but really beautiful underwater views of the fish and the coral reef around there and aside from the very small group we were in (just 5 passengers total) there was no other tourist boats nearby. We sailed out of Port Douglas on a Chinese junk which was an amazing experience, unfortunately, that boat is no longer operating, but there are other small charter boats that make scuba and dive trips and it's a terrific area if you want to avoid the crowds that come with the large boats like Quicksilver.