What does playing as your pet mean?
Playing
 as your pet basically means that by clicking a button your wizard will 
disappear and instead you’ll be controlling your pet, it costs 5 
happiness per 1 minute of playing as your pet.
Is playing as your pet useful?
Yes,
 playing as your pet is needed to complete a few quests, one of the 
quests is for low lvl wizards which gives them a pet for completing it 
and a few quests in Karamelle.
This is how playing as your pet looks like:
 How to use play as your pet?
- Click on the pet icon that’s next to your energy.
- You can choose the play as your pet option.
- You
 can choose to recharge your pet happiness by giving him snacks, that’s 
the only way in-game to replenish your pet’s happiness, snacks that will
 be used towards pet happiness won’t raise your pet’s experience nor 
their stats.
- You can inspect your pet, but clicking the letter “i” is basically the same thing.
- When
 in the play as your pet mode, you can either cancel it or make your pet
 dance (which as of right now is pretty much useless, besides 
amusement).