I can see where this might happen. My mom was very tall for her time, and she would tell tales of people thinking there was something wrong with her, because she didn’t act the age her size implied. (I never asked her mom, he would have been 5’ 11" before 1920, how she was treated.) Ironically, 4 of my kids have/are all been small for their age, even though I am 6’ 2". (I grew late, and I married a very short woman, so we have no idea how big my kids will end up. Well, the almost 17 year old is finally maybe 5’ 9", so he is no longer extremely small. The endocrinologist we took him to when he was smaller than everyone but a girl whose mom was 4’ 11" said he would be 6’.)
A few of my kids have had trouble making friends. The oldest two are twins; both had trouble making friends at the Kindergarten age. Most kids that age can only be friends with one kid at a time, although who it is might change in a few hours. Twin 1 said that the following conversations hurt: “Will you be my friend?” “No thanks, I already have one.” That one, was sometimes twin 2. In HS, the twins were best friends with two girls, and basically had no other friends until their senior year. This was good for twin 2, who is very introverted and shy. She only needs a friend or two. Twin 1 is introverted, also, but loves college, because she made many friends immediately. So, eventually, she made friends. But, the last 12 years or so would have been tough w/o the one friend who has been a friend since first or second grade. (They knew each other before kindergarten.)
I think the Daisy troop idea is a great idea. You can gently help your daughter socially, and give her a chance to consistently interact with other girls.
I think advancing a grade is a bad idea, although it can work out for the right kid. It sounds like your daughter has some social development to do first. We rejected skipping grades for our kids. At least in our area, they can take classes geared to their level. We have a great GT teacher at the local elementary school who made sure kids 3, 4 and 5 were not bored. (She was hired too late for the twins.) The middle school worked hard to make sure Kid 4 could take math at the HS while he was in MS, as will Kid 5 next year. Right now, I have a textbook I am supposed to review for the HS, so kids like mine don’t have to go to the local college for math. (Twin 1 missed out on any shot at valedictorian because college classes didn’t count towards her GPA.) If your area is similar, and one nice side effect of the no child left behind act is that schools now bend over backwards for good students, you should be able to keep her academically, and socially, where she needs to be.