Listed as follows in Alphabetical order

Alligator > hatchling
Armadillo > pup
Bad > pup
Badger > kit, cub
Bear > cub
Beaver > pup, kitten
Bee > larva
Bird > hatchling, chick
Boar > piglet, shoat, farrow
Buffalo > calf
Butterfly > caterpillar,larva, pupa, chrysalis
Camel > calf
Cat > kitten
Cattle > calf
Cheetah > cub
Chicken > chick, pullet, cockrell
Coyote > pup, whelp
Crow > chick
Deer > fawn
Dog > pup
Dolphin > pup, calf
Donkey > colt, foal
Dove > squab, chick
Duck > duckling
Eagle > fledgling, eaglet
Echidna > puggle
Eel > leptocephalus
Elephant > calf
Elk > calf
Falcon > chick
Ferret > kit
Fish > fry, fingerling
Fly > maggot
Fox > kit, cub, pup
Frog > tadpole, polliwog, froglet
Gerbil > pup
Giraffe > calf
Gnat > larva
Gnu > calf
Goat > kid, billy
Goose > gosling
Gorilla > infant
Grasshopper > nymph
Guinea pig > pup
Gull > chick
Hamster > pup
Hawk > eyas
Hedgehog > piglet, pup
Heron > chick
Hippopotamus > calf
Hog > shoat, farrow
Hornet > larva
Horse > foal, colt, filly
Hound > pup
Human > baby, infant, toddler
Hummingbird > chick
Hyena > cub
Jellyfish > ephyna
Kangaroo > joey
Koala > joey
Leopard > cub
Lion > cub
Llama > cria
Louse > nymph
Magpie > chick
Mallard > duckling
Mole > pup
Monkey > infant
Moose > calf
Mosquito > lnymph, wriggler
Mouse > pup, pinkie, kitten
Mule > foal
Opossum > joey
Ostrich > chick
Otter > whelp
Owl > owlet
Panda > cub
Parrot > chick
Peafowl > peachick
Penguin > chick
Pheasant > chick
Pig > piglet, shoat, farrow
Pigeon > squab, squeaker
Platypus > puggle
Porpoise > calf
Prairie dog > pup
Pronghorn > fawn
Quail > chick
Rabbit > kitten, bunny, kit
Raccoon > cub
Rhinoceros > calf
Sand Dollar > larva
Sea Urchin > larva
Seal > pup
Seastar > larva
Serval > kitten
Sheep > lamb, lambkin, cosset
Skunk > kit
Snake > Snakelet
Spider > spiderling
Squirrel > pup, kit, kitten
Swan > cygnet, flapper
Tiger > cub, whelp
Toad > tadpole
Turkey > poult
Turtle > hatchling
Wallaby > joey
Walrus > cub, pup
Weasel > kit
Whale > calf
Wolf > pup, whelp
Wombat > joey
Woodpecker > chick
Yak > calf
Yellow Jacket > larva
Zebra > colt, foal


Not precise but simple rules

Baby bird --> chick
Young canids --> pup
Young felines --> kit, kitten
Baby herbivors --> calf
Baby insect before metamorphosis --> larva
Baby insect after metamorphosis --> nymph, instar
Just hatched bird and reptiles --> hatchling


Any other rules can be found?