I searched around a little bit, and I couldn’t find the base animals I feel games like this might have—chickens, cows, and sheep, not to mention goats and mice. But, since this looks like it’ll start in the ‘pre-historic’ period about somewhere in places that resemble the Old World, perhaps animals like aurochs or mouflon. Or, if you really would like to go way back (according to Uniformitariansim and Evolutionism), you might as well have the Giant Sloth and the woolly mammoth. Maybe with mods, we’ll have dragons, leviathans, etc., but I think animals like these should go in this game.
Of course, some of you may say that having this wouldn’t be good for children when it comes to killing them, but who ever said there would be blood? It could be a health system like Minecraft or BotW (there we go again, yes), and possibly a mechanic that lets them heal, perhaps even a weariness bar! Then, they’ll simply drop their items (or it goes directly to the inventory of the entity that killed it), and then you can fry your baco—mutton.
Of course, there’s also the vegetarian way, and they may only be able to provide flesh for predators. Then, there’s the absolute vegan route, and they are simply pets/decor to your world. However, I quite like the more realistic idea of them being able to be domesticated (here goes that BotW stuff, yet again!), included with a domesticated level that goes when you sooth, feed, and protect them from predators.
Now then, many of you will also say that this may go with mods, but the base idea is something that could be added from the very start—just that “purely vegan” approach at first, so the modders could then add functionality and/or more animals.