jai'galaar: shriek-hawk
galaar: hawk
gi: fish
nuna: swamp turkey originally from Naboo
(Mentioned in 501st and Revelation.)
senaar: bird
shatual: large deer-like animal native to Mandalore
(Mentioned in True Colors and 501st.)
striil: hunting carnivore native to Mandalore
uliik: mount, pack animal
(Also spelled ulik.)
vhe’viin: field mouse native to Mandalore
(Mentioned in 501st, Order 66, and Revelation.)
agol'oy: fauna, animals in general
akaan'uliik: rock-lion
durik: vermin
oyarak: any large carnivore
ricya: domesticated feline predator, cat
rish'ak: wild cat, feline predator
sen'cya: domesticated bird
vorparak: any large carnivorous plant
Cats
Tuuka (a more Mando'a spelling of tooka) is a cat-like animal and often used to refer to an Earth cat, but it's not in the standard dictionary.
Dogs
Striil is a large animal with dog-like habits. People often use it to refer to an Earth dog or another large animal who acts like that.
General terms for pets
When using Mando'a among other Earth Mandos, use whatever you would normally use for your pet's species in English (or other word if speaking with others using a different mutual Earth language), instead of coming up with a clunky new term. Alternatively, using the pet's name works well, and people love seeing pet pictures.
For animals in fan fiction, use a Mando'a word closest in description to what you want to talk about, or use the Star Wars term for that animal. Add orikih (tiny), kih (small), or ori (big) if needed to offer a closer description of the desired animal.
Many people consider their pets to be their friends or children, so burcy'ika (affectionate term roughly translating to "little friend"), ad'ika (little one), ik'aad (baby), or verd'ika (little soldier, when used outside of the military) could work. In one of the novels, one clone tells someone that cyar'ika is sometimes used as a term of endearment for a beloved pet.
The closest equivalent for a wolf in the core dictionary is striil; Wookieepedia article: https://starwars.fandom.com/wiki/Strill
alii'oya, from the unofficial Star Wars Legacies: The Force Eternal Role Play site: https://thestarwarsrp.com/index.php?threads/aliioya.74903/
dha'karir, from the unofficial Star Wars: Exodus roleplaying game: https://starwars-exodus.fandom.com/wiki/Dha%27Karir
laaran oya'kar, from the unofficial Star Wars: Exodus roleplaying game: https://starwars-exodus.fandom.com/wiki/laaran_oya'kar
kyr'oya'kar, created for a fan fiction series: https://swfanon.fandom.com/wiki/Mandalorian_wolf_(DKW27)
kurs'kaded, from Tal'jair: http://mandoa.ru/eng
wolov, based on the Mando'a spelling of the Earth word