One special filter in the "My Inventory" screen is the Pet filter. Pets can be carried in your Pirate's inventory.
There are many pets to collect in Pirate101. They’re available in many ways: from the Crown Shop, as rewards for badges, as rare loot from powerful bosses, and more.
To equip a pet, find it in your inventory and equip it by double-clicking on it. Once you have a pet equipped, that pet has a chance to join you in combat! You won’t be able to control it, but it’ll do its best to help you out.
If you’d rather have your pet follow you around the world, instead of your Firstmate, open the Options screen, select the Gameplay options, and find the option called “Follower Is.” Choose “Pet,” rather than “Firstmate”, as seen below: