Tom Clancy's The Division will indeed include dogs, just not doggie companions.
Ross-Edwards joked in response to a question if the game would have canines, "Well, it’s a next-gen game so obviously it’s got to have dogs!"
He then added seriously, "No, dogs won’t have any special significance other than the fact that New York has over 300,000 dogs living in the city, so imagine if they are all let loose at once… You may encounter some particularly nasty ones. But no they don’t play a significant role."
So, there are no dog companions like other games, but you do get to shoot them. C'est la vie.