My little one will be 2 this September and I am trying to understand some of her behaviors. She is very friendly and can be overly accepting of strangers, and she has never really had an issue with separation anxiety. She waves and blows kisses to everyone, from the well-dressed business man to the man with one shoe and raggedy clothes. The issue is that when I put her around children her age, she will not socialize. It's almost like they aren't there.
Children around 1 years old are often not very social with one another and they may not distinguish strangers from familiar faces, which is why they wave and smile at the whole world. It takes children quite a while to figure out how to interact with peers. Even a child who is 2 or 3 years old may not really socialize with others but play in a solitary way side-by-side with another tot.
Some questions to consider about why your daughter may be shy around kids her own age: In your own interactions with your her, does she connect with you in a warm, humorous, and mutually interested way? Have you raised your daughter differently from other kids you may have? Have you given her many opportunities to play with other toddlers?
Aim to arrange plenty of occasions (playdates, birthday parties, trips and outings, etc.) for your daughter to spend some time with other little children and observe whether she begins to interact and resemble them more in social situations. If your daughter still seems to be a bit different from other kids, consider asking your pediatrician or family doctor for more advice.