I recently got a female pitbull that's just over two months old. Sometimes, while she is sleeping, she will begin to twitch and make noises. It almost looks like she is distressed - like she is having a bad dream. Should I wake them up in this case?
Dogs are just like us. They dream like us and it's a healthy way to deal with what's happened during the day. However there's no evidence that they have nightmares. But it's important for that process to happen undisturbed. Your dog is likely dreaming of a rabbit chase. All this is perfectly normal.
Interesting article there https://terriblyterrier.com/can-dogs-have-nightmares/
Dogs do dream as stated earlier. They will yip and quietly bark in their sleep while dreaming and will move their legs by twitching or to appear as running. It's perfectly normal and just like a human doing the same in their sleep. There's no need to wake them or disturb them. They just are enjoying a good dream of chase or taking a swim.