Well, if I remember correctly all rides have a safety device, either a bar or a belt, even it's a small world. I think a better criteria would be if it's the sort of ride that is apt to throw you against the safety device.
In a way this is compared to riding in a car during which you wear a seat belt. The chances of you being thrown against the safety device at most of the Disney rides and being injured is less than that for riding in a car. I've never heard of injuries caused by Disney rides.
Now you probably wouldn't want to ride a roller coaster or one of those midway rides that swirls you really fast. But I've ridden the Disney ride in which you're in a boat and go thru a mountain. There is a bar but if you hold onto the bar to keep yourself from slipping you won't hit it.
I wonder if your doctor has ever been on rides at Disneyland.
Relax and have a great time! The likelihood of you or your baby being injured are extremely slim especially if you're selective and avoid high speed rides that throw you around. Disneyland rides geared towards kids are not like midway rides. They may have some of those but you can avoid them.