However, combat has absolutely nothing to do with leveling a pet. You just need to summon your pet from the deed and it will automatically level as time passes. You can leave it in your datapad and it will still level. The import thing is you tame it from the deed. Don't worry if you don't see any changes when you click on your pet in the datapad, the visuals showing the stats won't update until you summon the pet but it's still growing.
You are correct, I apologize - I was thinking of the CH grind I went through lol. Thank you for correcting this for everyone else!