A pet agreement should include the landlord's and tenant's information, the place where the tenant will live with their pet, the inclusive dates of the contract (start date and end date), as well as how many pets are allowed within the property, and specify the amenities where the pet(s) are allowed.
Deposits are completely normal. Some breeders even ask for them in order to be put on the waitlist. They help the breeders to know who is serious and to know that the puppies definitely have a home.
Be aware that most contracts in the dog world are not legally enforceable, especially the ones that are micromanaging. Legally, dogs are property. As a result, do not rely on contracts to ``force'' the behavior that you want. Instead....