Yes, your daughter was authorized to drive the car, because she was authorized by someone who 1) herself had the authority to drive (someone authorized by the vehicle's owner can in turn let another person drive) and 2) whom (as the daughter of the owners) your daughter would reasonably believe to have authority (which means she had apparent authority, and other people, like your daughter, may rely on and act in accordance with the reasonable appearance of authority).The above said, IF your daughter was at fault in the collision, she could still be liable: the owner of a car may recover compensation from an authorized driver who is at fault in damaging the car. So if your daughter hit the deer because she was inattentive, driving distractedly, driving too fast, etc., she could be liable.