@newhere You got great answers already. It seems worth it to discuss it with a specialist and keep an eye on her development, but the main issue to me is distress. Is she having distress about her relationships? Is she anxious? Is she having problems in school (grades)? Does she feel lonely? Does she feel bad because she can't connect with others? Is she bullied at school? From what you wrote, it seems that most of the answers are no, so that would be a reason to not seek something medically "wrong" with her.
The other part is that autistic people don't lack empathy (knowing what others feel or feeling what others feel). As you can tell from all the answers here, there is plenty of empathy. The issue is often not
expressing empathy in the way most people do.
To this day, I hate pictures of me being taken. Since I was a little kid. I hated pictures. I have no clue why. I also daydream to a professional degree. I'm often distracted because I'm thinking. When I was a kid, my parents would find me sitting as if I were dead, but I was thinking. I used to have an imaginary alternative world. I never touched or hugged my mother, but I'm (mostly) ok hugging a girlfriend and being intimate. I had and have problems connecting with people, but things are mostly fine. Thankfully I grew up at a time and a country in which kids were not labeled, so I was left alone. I'm a professor now so for all practical purposes my life is fine.
I should add: I had a lot of problems connecting in school/outside my comfortable bubble. But understanding people was and is a special interest. I eventually became good at understanding how to be charming, etc. But it takes energy and doesn't come naturally. If you know me well, you know I wear elaborate masks.
You're doing the right things. Loving and worrying about your daughter.