I agree with AlecM, most pets are not given tranquilizers. Most small pets are pretty quiet when their owner is near by and they are in small carry bag anyways. WindFlyer is right that pet owners are considerate of their fellow passengers so I wouldn't worry too much about it.

As almost every airline offers some easy way to bring pets on board and as more and more people travel with their pets, you are bound to see more four legged flyers throughout the cabin. Especially since United and possible others are giving an extra 1200 miles for PetClass travel too.