Queensland and Cairns
Hi, I'm a bit late on this thread, but I'll put in a couple of pennies' worth anyway.
My wife and I went to Australia for the first time last year at the end of April, beginning of May, flying into Cairns from Japan where we live. We were only there for nine days in total.
I asked for some advice here on BF, and one place people mentioned for birding was Kingfisher Park in Julatten, run by Keith and Lindsay Fisher, (pure co-incidence on the name, I believe) which we recommend.
http://kingfisherparkbirdwatchers.blogspot.com/
We enjoyed our three-day stay there very much. However, it rained most of the time, though the rainy season was supposed to be over (we were still the only guests), and apart from the rain itself, an hour or so of light was lost at the beginning and end of each day because of the cloud cover. We did get to see quite a lot of birds one way or another - Mount Molloy is a short drive away, and has a quite different climate and birdlife, and we went to other nearby places also - but it might be better to get some advice from Keith Fisher direct as to when would be a good time to visit north Queensland during the time you have available.
You are going one month earlier than we did, so adjust everything accordingly - i.e the rainy season in the north will definitely still be ongoing, but there will be birds there when you go that had left by the time we went at the beginning of May (such as the buff-breasted paradise kingfisher, and Cairns shorebirds).
We stayed in Cairns for a couple of nights and got quite a lot of birds (30 or so species) on the foreshore even though most of the shorebirds had gone north already.
We also went inland over the Atherton Tableland to Undara Lava Tubes. Having based ourselves in Cairns and having only a short time in Australia, we wanted to see some dryland also and some kangaroos, and maybe other things. Undara was a long drive and worthwhile for us, but I wouldn't recommend it if you have seen kangaroos elsewhere in Australia - the accomodation is also rather expensive, though fun (railway coaches), and the food not very good. We saw some birds we wouldn't otherwise have seen, but if you saw dry land elsewhere in Australia, you will probably have seen these birds. The Atherton Tableland is probably worth more time than we were able to give it: in two hours at Hasties Swamp, we saw ten species we didn't see elsewhere, for example.
If you go through Cairns, then taking the boat out to Michaelmas Cay and spending as much time as possible there snorkelling (there may be four or five species of birds also that you won't see on the mainland) is something you absolutely should do. We recommend buying in Cairns and taking your own sandwiches and eating them on the beach, because otherwise going back to the main boat for lunch (included in the ticket) will take an hour of your time minimum, and there is only four hours total at the Cay because the trip takes about two hours each way. The snorkelling is better than the diving, because the water is clearer at the surface, and there seem to be more species of fish. And rent a waterproof camera for $50 and take some photos of the fish you will see.
If you have only a short time in Cairns, then Green Island on the reef can be done in half a day, and although it's very touristy, there are still lots of fish and nice swimming.
From Cairns in ten days, you can get four environments: seabird foreshore, Great Barrier Reef, rainforest, and dry savannah (Undara).
In total, we saw about 120 species of bird in ten days, and we spent quite a lot of time doing other things - swimming, eating, driving (rental car), just admiring the scenery, and so on.
And the people in Cairns (even though it's almost all tourists) and Queensland generally are great, friendly, polite and generous. This was the thing that we both liked best about the place.