No, the pet lives in India with the brother as quoted in the first post: "He resides at our family home in India and independently manages household responsibilities, including caring for our family dog".
If you want her to remain in the country for additional months, apply for a visitor record or extend her stay. Visitor visa is generally for entering the country.
Further reading:
https://www.canada.ca/en/immigration-refugees-citizenship/services/visit-canada/extend-stay.html