How do you indicate whether or not pets are allowed? This is done per object, in the object setup. In the type settings, you can set how many pets guests are allowed to bring, but this only applies if the booked object allows pets.
Use the 'pets' filter in the objects overview to quickly see which objects currently allow pets.
Allowing pets in the object setup
You can already indicate the pet status of an object when creating a new object. If you want to change this status for an existing object, go to the setup tab of the object in question. Here, you can edit a setup to change the pet status.
Read more: Editing an object setup
Whether pets are allowed has nothing to do with amenities. Yet, you may want to create an amenity for 'Pets allowed'. This will allow guests to use this amenity as a filter in your Search & Book.
Limiting the number of pets in the type settings
Open the type via the types submenu, and click 'Edit'. In the 'House rules' section, add a new line for 'maximum number of guests', and put 'pets' in the guest types field. This limitation will apply to all objects where pets are allowed.
If you set the maximum number of pets allowed to 0, that effectively blocks pets from being added to reservations, even if the underlying object does allow pets. So, it is not recommended to do this.