If you were wondering how to heal your pets like I was, this should help you! They added a couple of Pet Battle introductory quests in the last patch. Marcus Jensen, the Pet Battle trainer in Goldshire has them (not sure if the other trainers have any currently.)
First quest is to go out and defeat a wild pet. Once you've done that, he gives you a quest to talk to Erma, Goldshire's Stable Master. Turns out that Stable Masters are now Pokemon Centers, and can heal all of your pets for free! After healing, you can hand the quest in. You then get Revive Pets
as a reward!
So it looks like there will be three ways to heal your pets: Stable Masters, the Revive Pet spell and the Battle Pet Bandage
, which I have no idea how to get!