I appreciate your thoughts, and you seem sincere, but I am also wondering why you seem to be 'pushing' this gift on this girl and her father.
If he is a single father (and it sounds like he is) this could be one more straw on the camel's back, so to speak. He's probably got enough stresses and worries.
Maybe you could just buy an animal and keep it at YOUR place, so the girl has benefit of owning the pet SHE prefers without actually having to move it into her father's house. That way you can also supervise her with the animal, and show her how to care for it. You can also make sure the animal eats, stays warm and healthy...