Don't feel like you need to hesitate to list her accomplishments and milestones here. We're all parents of gifted children here, and we've all dealt with negative reactions from other parents, so this is one place where you can feel free to share without judgement. For instance, there's this thread:
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/28872/The_ultimate_brag_thread.htmlI don't have any Montessori experience to speak of, but from the threads on the subject I've lurked here, the results seem to be a mixed bag, dependent on the school itself, and the personality of the child. The strength of Montessori seems to be that it allows the child to progress at her own pace, and is child-led, which is perfect for gifted children.
The downsides are when the schools insist on keeping children in age-peer groups, which means you'd see your DD having the same kind of social problems she's experiencing now. Also, Montessori schools tend to be very rigid about using objects in very specific ways. Creative, spontaneous kids who like to repurpose objects and be funny are not encouraged.
So, before I'd enter my DD in a Montessori school, I'd take a good look at whether the school is willing/able to place her in a group with older children present, and whether my DD's personality is one where her spirit would be more likely to thrive or be crushed by a by-the-book approach to every task.