It really depends on how big the dog is. My dog Kiba is 22 ibs and she sleeps in the hammock with me. However, if she were any bigger she wouldn't. I highly recommend to people that have a medium to big size dog to do exactly what lazyriverroad mentioned
and let her sleep under the hammock. Just remember, dogs aren't like us with sleeping in places like hammocks. The only reason Kiba can sleep in a hammock is because I am in there with her. Also, it's like having another person in there with you when they are bigger and it's not comfortable at all.
However, after a lot of practice with getting her comfortable. We made it work and it's a lot of fun to have her out in the woods with me.