Do you think Southwest Airlines allow my dog on board with me?

I am going on vacation this summer to Disney World in Florida. I am taking Southwest and I must bring my papillon with me. She is roughly around 8-11 lbs. And if I don't take her, I have nobody to watch her. Do you think they would allow my dog to fly on the same plane as I am? I really want to know. I already found hotels in Orlando that accept dogs. Thanks so much for your help.