When I went into labour with DS, DD was 5 and she came to the hospital with DH and me. She was in the birthing room throughout my whole labour, but when I was rushed to the theatre for an emergency c-section, she was not allowed in. As a consequence, neither was DH because he had to stay with her. She said that she liked being there, and I had a good experience overall too. When DS was born, the hospital staff gave him to me to hold for a few minutes then took him to DH straight away, so DD got to meet her brother then.
I never considered not having her there. If your DD wants to be at the birth, I say go for it. Children are much smarter and much more resilient that we give them credit for.