I can throw some questions out there that a Canadian border agent may want to know:
(1) what is the purpose of your visit to Canada?
(2) why do you feel the need to travel with the pet?(dog or cat)
(3) how long do you plan to stay in Canada?
(4) which hotel(or friend/relative's house) are you staying at and are they okay with the pet?
(5) will the pet leave Canada with you?