How about you invite both your father and brother to visit you? Then your father and your brother apply the visitor visa together? If so, his FD & property can be counted as ties.
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