Absolutely normal and healthy! Some Kids start masturbating very early in life. There is absolutely nothing wrong with it as long as she knows that it is something to be done in private. She is just fine :-)
It makes a difference whether she is awake or asleep because there are some people this happens to in their sleep. Its a disorder just like sleep walking. If she is however doing it while she is awake then I would say maybe talk to her pediatrician see what they can tell you. Children do begin to develop and get curious about their body, that I understand but as far as masturbating at such a young age there might be a problem.
I think this is perfectly normal! An 11 year old is still discovering their body and seeing what all it can do. Masturbation is a normal part of life, even for children. Some kids start around age 5! Everynight is quite a bit, but maybe it is just a phase! I wouldn't worry about it.
When she is awake does that make a difference?
I would say this is not normal. Majority of the times when these things happen it is due to some sort of sexual abuse whether or not she remembers it may be the problem if she was very young. Also does this occur in her sleep or is she awake?