When I was growing up, I was the one who got things done. If there was a tragedy or death or something traumatic, I didn't cry or retreat under the covers. I had a friend who wailed and just shut down. But ever since I was a teen I was the one who got the meals organized, who called people to babysit for the family, etc. And during funerals, I helped my dad (he was a pastor) by driving his car so that he could ride with the bereaved family, helping arrange details with the funeral directors, and I organized countless post-funeral receptions and meals and errands.
I'm still like that. I am NOT the person you will get long comforting hugs, quiet bedside vigils, soothing words and lots of tears from. Of course, I can express my condolences appropriately and show compassion. And sometimes I cry later, much later.
But I know that my strengths lie in action, getting necessities accomplished, organizing help, thinking of details, enlisting assistance. While someone is sitting quietly, uttering soothing words, I'm getting groceries for the family, cooking, remembering to find out if they did this task or that (if Grandma is in the hospital, who's picking up her mail and who has canceled her weekly hair appointment, etc).
I think that some people are just like that. Nurses, for example, and emergency medical technicians and first responders. Yes, they may cry later but in the moment they are all business. It may seem uncaring to some. But the world needs all kinds - the soothers, the criers, the comforters, the detail-oriented, the stoic, the passionate. During a funeral, we need the people who sit and hold the hands of the grieving. We also need the people who realize that often during funerals, horrible cold-hearted thieves break into the home, knowing that everyone will be at the funeral, so these good-hearted people skip the funeral and maintain a presence at the home, probably mowing the lawn or washing the dishes.
It sounds like your daughter has a healthy balance - she cares, but she has a sense of calm during the storm.
I would worry if she didn't participate in things like the ceremony for the girl with the sick mom and instead complained that everyone was holding up the game. I'd worry if she couldn't show compassion to her friends and empathize with them.
Embrace her strengths and encourage her to develop her gifts - the ability to be compassionate but also to take action and be a source of strength and help. Calm in the storm. It's not a bad way to be.
My dd is a young adult, but she's always been quick to sob, to cry, and to fall apart. Her beloved dog died two years ago, but she still just weeps uncontrollably when a particular tv commercial comes on showing a dog that looks like hers. She'll think of something that reminds her of Grandpa (who passed away 15 years ago) and she'll cry.