ah, thats because turning is controlled by the camera, and not the capsule
the capsule controls movement in the sense of moving forward, backwords and side-to-side, but all rotation is done by the camera
You could take the "Mouse Look" script from that "standard assets" first person controller camera, and apply it to your own camera - or just copy the entire camera to your own dog
Just make sure the camera is parented to the dog itself
hope this helps