“The owner of any dog is liable for the damages suffered by any person who is bitten by the dog while in a public place or lawfully in a private place, including the property of the owner of the dog, regardless of the former viciousness of the dog or the owner’s knowledge of such viciousness. A person is lawfully in a private place when the person is on the property in the performance of any duty imposed upon the person by the laws of this state or the laws or postal regulations of the United States, or when the person is on the property upon the invitation, express or implied, of the owner.”