Well, maybe not a game as much as a tease/challenge. Feel free to answer, add or both…
Dogs have puppies
Cats have kittens
What does a fox have?
What does a hawk have?
What does a kangaroo have?
What does an owl have?
What does a pidgeon have?
What does a goose have?
Foxes have kits.
Kangaroos have joeys.
Geese have goslings.
An Aussie that doesn’t know what a Roo baby is called?
::Shaking head::
What’re we gonna do with you dpr?
-Sam
Kangaroos have joeys
fox have sox
Owls have owlets.
Pigeons and hawks both can have chicks but that’s no fun.
A goose has goslings.
You said add?
Whales have calves
Swans have cygnets
Mice have pups (or pinkies if feeding reptiles)
Did I say I didn’t know it?
I have all the answers so far.
How about we add:
What do Americans have?
A: Brats
ducks and covers
IIRC, raptors have eyases (singular: eyas).
Dogs have fleas.
I thought pigeons had squabs?
… and Tribbles have MORE Tribbles.
:: Ducks! ::
Deer have fawn.
Humans have, umm, infants.
What do you call the kids of an aussie?
You don’t, and hope they’ll stay where they are. The fewer Aussies we have here, the better.
Hey, at least I didn’t say “seething pile of kangaroo dung” 
Is it a new term? It’s not in my OED. How do you pronounce that?
OK, I got one:
What do you call baby fish?
Fingerlings. Or is that finger-licking good?
Uhh…That’s fish, not fish sticks.
I thought you had a sense of humour Audrey… sigh
Fingerling: n. any young or otherwise small fish esp. salmon or trout
Eyas: n. a young hawk esp. one taken from the nest for training in falconry
Extra-bonus thought: We don’t call them fish sticks in Australia - we call them fish fingers. Is this why?