it' sounds like a sensory issue.... take her to her doc. If he says she'll grow out of it.... FIND A NEW DOCTOR!!! it could also be the early signs of OCD. I would have her checked immediately.
I agree with "DustyL", this sounds like either Sensory Integration Dysfunction or Obsessive Compulsive Disorder. I would recommend taking her to a pediatrician to start with, then he/she can refer you to a specialist.
My mom still has a very mild version of this today....and I have seen my toddler going through a phase when he was so intense about completing a task that the other hand would do a similar motion. I blamed it on him being left-handed but later read that mirror movements are
1. a developmental stage in most children, if you think about it, even dogs have those movements, when they scratch themselves, the opposite paw wiggles with it...
2. can be an inherited trait and there are two forms. One is just a very mild case that can remain throughout adulthood but become less and less apparent, the other can be part of some neurological syndrome, forgot the name, but it comes with unusual physical appearances.
I am pretty sure it is still that common developmental stage for your daughter.