I am the oldest and my husband is the oldest. We both had imaginary
friends.
I'm a certified parent educator--It's very common for preschoolers (ages3-4) have im friends. In fact, it means that they are developing a nice sense of imagination. We should respect their im friends and not mock this stage in a preschooler's life. We do not want to take away their freedom to explore -- and their privacy of developing this.Usually first borns have imaginary friends.
This imagination is very cognitive, allows emotional growth, and helps the preschooler find out about her world.
Keep tv at a minimum and let her continue what she is doing at her own pace.
Still involve your daughter w/ a few playmates -- real ones --- on a weekly basis. And a few activities outside of home. **Very important!
Everything sounds a-ok ! Your daughter does well w/ other kids in school and does not isolate herself. That's great !
My kids are far apart in age. My daughter had an imaginary friend. It was a super experience for her. The only time I had to intervene is when she used the im friend to lie. (She was 4 then). I simply stated that it was not ok that she lied--but, she was still my best girl. She never did it again.