No it is not correct, unless "Three Dogs" is the name of something. "Oh, there is Three Dogs!" In this case Three Dogs would be a person or animal's name. Cheers
Simon; To sum up, you were right to trust what you knew to be correct. 'There is' is for singular use, 'there are' is for plural use. Bad English is common. Our mission, should we decide to accept it, is to help preserve this wonderful international language from linguistic vandalism - lest confusion reign.