Cape Tribulation Tropical Research Station
The Cape Tribulation Research Station in the heart of the Daintree Rainforest—one of the oldest rainforests on earth, where the coastal jungles of Queensland meet the Great Barrier Reef—is one of the only tropical forest research sites in Australia. It is the only one in Daintree, as far as I could find, that accepts nonacademic visitors.
Cape Tribulation is purely an active research station. Hobbyists and wildlife enthusiasts are not part of their business model, but they are willing to accept non-academic volunteers on a case-by-base basis.
Their PDF lays out what is expected of these volunteers and the kinds of projects and daily activities carried out.