Well, call me the contrarian, but a dog being placed in the backseat of an aircraft unbelted is not only cruel to the animal, but also a real danger to the flight.
I hit clear air turbulence in a Bonanza one time last year and, despite being buckled in, still hit my head on the ceiling of the cockpit. Fortunately my headset band took the brunt of the impact. The box of IFR charts was thrown off the copilot seat and spilled all over the floor of the cabin. I shutter to think what would happen had a dog been with me during that flight.