Hi, I remember playing with a Ouija board at slumber parties when I was a girl. I recall being scared, but also excited and enthralled with the possibility that we were talking to spirits or ghosts through the game (we also played "Light as a Feather" and watched scary horror movies back then). I don't recall being traumatized or harmed by this experience, but am interested to hear how child psychologists and other developmental specialists will respond to your question.
I'm now the mother of a second grader, and would not encourage my daughter to play this game until she is older. She's still afraid of the dark, particularly ghosts and monsters, and she occasionally has nightmares, so I think playing this game wouldn't be good for her right now.
Use your instincts with regard to your daughter, and talk to her pediatrician about your questions and concerns too. Depending on your religious tradition, you may also want to consult spiritual guides (your priest, preacher, imam, rabbi).
For general info, here are some related links I found online: