1 Imperial Panda (Bear) 2 Tigers 3 Birds of Paradise (which are neither Magpies nor Phoenices) 4 Horses (which are not in the cycle at all) 5 Serpents 6 Turtles 7 Cranes 8 Dogs 9 Monkeys 10 (nothing) 11 (nothing) 12 not-Whales (or, perhaps, not-Phoenices)
Not in the menagerie: Butterflies, Foxes, Magpies, Spiders (or Dragons), Phoenices (but they're like Whales). 2 empty spots (because they insist there would be 12 whales, if there were any), 2 non-Cycle-related (that we know of) animals. By the way, this numerical order does not obviously correspond to Cycle order.
Significant? ....you decide.