A detachable carrier for small pets that can be attached to vehicles, such as bicycles, motorcycles, motor scooters, ATVs, golf carts or watercraft. The carrier allows not only for the transportation of the pet, but also for the enjoyment of the ride, by way of an open top hatch through which the pet can extend its head allowing for an “open air” ride and visibility. The carrier for transporting a small pet on a vehicle includes a box-like container provided with an upper opening that forms part of the container top. The opening has padded edges and is large enough so that an animal such as a dog can stand up in the container with his/her front legs on the padded front edge. Anchoring structure on the container bottom is arranged to detachably couple to a luggage rack or support plate on a luggage rack that is mounted on the vehicle.