You did not mention the age of your son.
Having a pet dog, cat, hamster, whatever, requires a long-term, multi year, commitment to the care of the animal. I have seen pets neglected and dropped off at the local animal shelter when the owner/care giver lacked the responsibility gene and the parent was busy enough simply caring for the child, let alone another life form to feed, care for and clean up after. The poor animal is the one that suffers and may be ultimately euthanized.
Big decision with long term consequences.