In law, pets are chattels (personal property). Pets are possessions you can give away like you can a couch, car, or tennis racket. This, of course, is not how pet owners think of their furry friends. A lot of people think of their pets as members of the family.
Animals do not have the legal status to own anything. You cannot leave money to a cat or dog, but you can still support them in your will.
The simplest plan is to leave your pet to a person you trust to care for them (talk to that person first) and leave your pet’s caregiver enough money that your pet is not a financial burden on them. If you don’t have a specific person in mind to care for your pets, you could consider the Ottawa Humane Society’s pet stewardship program. It is designed to ensure your companion animals are adopted into loving homes after your death (Ottawa Humane Society: pet stewardship).
Slightly more complex, you can set up a testamentary trust to support your pet for as long as they live. As trusts must have an end date, you would designate someone (perhaps a charity like the Humane Society) who would receive the money left in the trust after your pet’s death.