I'm sorry there's no particular order. I tried to order it like pet, then farm, then wild but it kinda failed.
Animal - Tier
Pet - Haustier
Wild animal - Wildtier
Insect/Bug - Insekt
Zoo - Zoo
Cat - Katze
Kitty - Kätzchen
Dog - Hund
Puppy - Hündchen / Welpe (Welpe is basically a baby dog, if you just mean a small dog you say Hündchen)
Bunny - Hase
Rabbit - Kaninchen
Hamster - Hamster
Cavy - Meerschweinchen
Mouse - Maus
Rat - Ratte
Fish - Fisch
Frog - Frosch
Tadpole - Kaulquappe
Turtle - Schildkröte
Cancer - Krebs
Crab - Krabbe
Scorpion - Skorpion
Bird - Vogel
Budgie - Wellensittich
Eagle - Adler
Butterfly - Schmetterling
Horse - Pferd
Foal - Fohlen
Cow - Kuh
Calf - Kalb
Pig - Schwein
Piglet - Ferkel
Sheep - Scharf
Lamb - Lamm
Chicken - Huhn
Turkey - Pute/Truthahn
Goat - Ziege
Elephant - Elefant
Lion - Löwe
Tiger - Tiger
Giraffe - Giraffe
Leopard - Leopard
Cheetah - Gepard
Bear - Bär
Polar bear - Eisbär
Penguin - Pinguin
Zebra - Zebra
Hyena - Hyäne
Crocodile - Krokodil
Hummingbird - Kolibri
Ant - Ameise
Spider - Spinne
Bee - Biene
Wasp - Wespe
Hornet - Hornisse
Bumblebee - Hummel
Camel - Kamel
Hippo - Nilpferd
Rhino - Nashorn
Manatee - Sehkuh
Whale - Wal
Shark - Hai
Jellyfish - Qualle
Pelican - Pelikan
Snake - Schlange
Caterpillar - Raupe
Worm - Wurm
Ostrich - Strauß
Monkey - Affe
Vulture - Geier
Louse - Laus
Owl - Eule
Kangaroo - Känguru
Buzzard - Bussard
Moose - Elch
Deer - Reh
Wolf - Wolf
Squirrel - Eichhörnchen
Dolphin - Delfin
Squid - Tintenfisch
Dinosaur - Dinosaurier
Unicorn - Einhorn
Human - Mensch
What's your favorite animal? - Was ist dein Lieblingstier?
My favorite animal is ..... - Mein Lieblingstier ist .....
I have a dog - Ich habe einen Hund
I have a cat - Ich habe eine Katze
I have a rabbit - Ich habe ein Kaninchen
* * * * * * * * * * * * * *
I hope I didn't miss anything out :)
What's your favorits animal? Comment in German :)