I'm not 100% sure, but I think I was around 5 when my parents got us a bunk (my brother who was sleeping underneath was about 3. It was not a problem. They left a little night light on so that I could see what I was doing when climbing in and out at night. I loved it.
Bunks usually have guard rails so the kids can't roll out. And if they can safely climb in and out, I can't see a problem. If you are concerned, you could ask you child to call out for you at night rather than climbing out herself. just for a week or 2 to see how she is doing with it.

Saša