In a couple of the Adventrues of Sherlock Holmes, a dog cart is mentioned. I have heard of small carts being pulled by a dog, but doubted that in the stories that was what was being referred to. My dictionary gives as second meaning, a type of cart, with small carrying compartment for a sportsmans's dog.
dogcart
n.
1 a small, light cart drawn by dogs
2 a small, light, open 19th-cent. carriage, usually with two wheels, having two seats arranged back to back: it originally had a box under the seat for a sportsman‘s dog

In the story, a second mention says it was pulled by a horse.