How old is your daughter? It's not unusual for children, particularly when they are very young (i.e., pre-school to first grade), to indicate play and friendship preferences of the opposite gender. This is not so typical as children get older. With a girl, the major issue isn't so much one of being a 'tomboy', but rather wheter this is accompanied by negative self-perceptions about being a girl. Your note indicates that your daughter does carry such negative appraisals, and this can be a problem. I'd proceed with an evaluation by an experienced pediatric mental health professional (clinical psychologist, clinical social worker, e.g.) who can help figure out how your daughter perceives the world, particularly gender issues.
Our daughter is 10, she will be 11 in August. Our 6 year old thinks her sister is "weird", and as of yet has exhibited none of these behaviors.
I should add that the older, Erin, has displayed these behaviors off and on through most of her life. She usually curtails them and acts more "girlish" when other kids start picking on her, but this time she seems to really be hanging onto it regardless of what other children think.
We've asked her if she sees anything wrong with being a girl, and she says she doesn't, but that she just doesn't "feel like a girl and never has". In her school, they've started basic sex ed/human anatomy and though she understands what puberty is and what happens, she thinks and hopes she'll grow a penis and can't wait to start puberty because of that.
She really seems to be psychologically male. Her mannerisms and walk are boyish, her voice is low for a young girl, and the way she handles emotions seem to be more male than female. I know there's a broad spectrum, but she's much "tougher" than other girls. We had her to an endocrinologist when she first started this behavior and he found nothing wrong, that she is a normal biological female.
I don't want to take her to a mental health professional because that might give her the impression there is something wrong with her. But OTOH, if she really is transgendered and identifies with a male personality, I think that needs to be looked into.
With adolescence on the near horizon, definitely seek help. Now, it may be hard to locate a clinician with a specialty of gender identity issues, but certainly make the attempt. Leave it in the hands of the clinician to help with with perceptions she might have about utilizing mental health help.