Finger, Moldoff and Kaye expand the Batman Family as they introduce Ace, the Bat-Hound in Batman 92 (June 1955).
Batman and Robin rescue a drowning dog, and put an ad in the newspaper, publicly announcing that Bruce Wayne has the dog. Later, when they drive the Batmobile out, the dog follows them. Rather than stop and take it back, even though they have just left the cave, they decide they do not have time for that. But stop anyway to bring the dog into the car. So that no one will recognize the dog, and realize Batman is Bruce Wayne, Robin makes a bat-mask for the animal.
And so the Bat-Hound is born! While Batman is on the trail of counterfeiters, Robin and Bat-Hound rescue a lost child from a pipe.
But Ace does not truly earn his place in the Batman Family until he single handedly (paw-edly?) tracks and frees Batman and Robin, who had been captured by the bad guys. Ace’s mask then falls off, but Batman pulls out a photograph of Bruce Wayne giving him (really Alfred in the costume) the dog. The fact that he was carrying that photo around would make me more suspicious, but apparently everyone just goes along with it. Batman then returns the dog to its owner, John Wilkers.
This story must have been wildly popular, as Bat-Hound would return in a few months, and go on to become a regular supporting character in the book.