This will be too much OP for some classes and will give us hell to balance the game.
Greetings,
I agree. I would avoid giving pets abilities that would impact combat. This creates a balancing issues and a meta of pets to where everyone would be running around with the same pets essentially.
My suggestion would be to give pets flavor by adding in quality of life abilities that do not affect combat. Here is an example:
Parrot - While summoned, your parrot keeps you supplied with a half eaten and stale cracker which he is willing to share with you every 2 minutes, restoring 60 percent of your health over 10 seconds while out of combat.
Bearan Cub - While summoned, your Cub playfully bites your mounts back feet, increasing mount speed by 5%
With love,
Joda