Ideas for a Pet Champion design

The way I see pets working is if it goes off something like, if you get attacked by a certain amount, then it comes to you and either protects you (i.e shields you if you get hurt, like it takes the damage instead if you're hurt for a certain % of hp or under a certain amount) or starts fighting off the enemy. Could use it's own certain abilities when you use a certain ability but has it's own internal cooldown for when it's allowed to use it again, it would also create a certain synergy with your champion and the pet and make you feel as if you're actually working with the pet. I don't know how it would want to function on it's own without basic input to guide it, maybe it just follows the champion a certain amount of units behind it when said champ is out of combat for whatever time that way it's technically always near you, and then if it's a certain amount of units from you, maybe it runs off or it prioritizes to path to you again. You could use a trinket as a basic way to command it or maybe the trinket or an item makes the pet play a certain way like an attack trinket, defense, utility, and etc. Lots of approaches, but I guess it depends on what type of pet they would want it to be.

Would be cool to hear some input on these ideas, improve them, change them completely, add something to it?