Though they inhabit the many undisturbed rivers up and down Australia's verdant east coast, platypuses are so shy and retiring that few Australians ever see one of these eccentrically evolved icons in their natural state. Visitors get lucky occasionally, spotting a bill and a fuzzy back along a riverbank, but to reliably find one of the world's only monotremes – egg-laying mammals – animal lovers have to head to the northern reaches of Queensland and the clear waters of the Mossman River.

The Mossman trickles down from the coastal range near the tropical resort town of Port Douglas. Up there, the trees and leaves of the Daintree Rainforest strip vast amounts of tropical moisture out of trade wind-propelled clouds moving eastward from the Coral Sea, then send the water rushing back toward the Pacific via the river channel. The Mossman has been so well preserved that its swift-moving waters are as potable as they are clear.

Barney Marris, owner of the Back Country Bliss outfitters, takes visitors on trips to snorkel the Mossman. After donning neoprene wet suits and boots, adventurers swim through the narrow channels and hike across the sandbars of the river. Barney points out the more garrulous fauna: rainforest lizards, snakes, small fish. The sights are lovely, but no one comes here to see small fish.

The platypus is the king of this jungle, but he's a very reserved sort of regent. The species is rare, nocturnal, and profoundly wary. So platypus enthusiasts have to hit the river early in small numbers, and they have to creep along carefully.

"I usually see them in the early morning when I do a check on the river conditions for the upcoming day's trek," says Marris. "If you're willing to get up early enough, it's good odds we'll see one or two."

And what a sight. The platypus is likely the strangest of all mammals. It appears to have been stitched together from the spare parts of woodchucks, ducks, geese, and beavers. It has no nipples, and the male of the species emits a venom through spurs on its hind legs. To see one is to feel the urge to giggle and marvel simultaneously while thanking providence for the chance to witness something so furtive and unique.

More information: An hour north of Cairns, Port Douglas is a coastal hub that provides access to both the Great Barrier Reef and Daintree National Park. The Newport on Macrossan offers well-appointed rooms from $120 a night.