Polpetts!

Introducing...Polpetts! A new pet type for Minecraft. Hatch an egg! Keep the little goober happy and fed!

They can be found in buried Polpett Gardens, a generated structure that can appear beneath Oceans, Mountains, and a few other select biomes. Upon acquiring an egg, it may take a long while to hatch, but fortunately you can pet it to try to speed up the process a tiny bit!
You can also craft an Egg Incubator, which speeds up the process when a Polpett egg is placed on top of it. Egg Incubators are also a Villager profession station, that of the Polpett Researcher. You can trade for things like cosmetics and even alternate colored Polpett Eggs!

This mod is mainly meant to be a small thing, to supplement a much larger gameplay experience, like a vanilla playthrough or a modpack. It is designed for people like me who have been craving a mod like this, appealing to the specific niche of people who enjoy the Chao Garden from Sonic, or pet sims/Tamagotchi in general.

Tip: Right click is your main way of interacting with a Polpett, and depends on whether you are sneaking or not. With an empty hand, you will either pet the Polpett (Raising Happiness but not satiating Hunger), or check it's status of the two stats. With something in your hand, you will either feed it to the Polpett (Satiating Hunger but not raising Happiness), or check whether it can be eaten. (Also, sneak right click to equip or unequip hats.)

As of 1.1.0, You can now put Polpetts in buckets! There is also a new biome that Polpetts can be found in.