Are dogs allowed on the trail? And are there many bear incidents on the AT?

Look at each portion. Some places is no. Smokey Mountains is a no and another place but can't remember the name of it. I've seen people say you have to board your dogs and have them drove to the next location for you on the parts they're not allowed.

Yes, dogs are allowed on the Appalachian Trail; just it would really be recommend that they be on a leash. It really depends on where you are. But there are for sure bears around, so just be cautious if you see one.