What time do you put her to bed? If you put her to bed early, that may be why she doesn't need the nap. I would back up her bedtime to 9:00 (not all at once) and see if that makes a difference.
If that's not the issue, find out what your local school does for kindergarten. Do they require nap time? If they do, you can't force her to sleep if she can't sleep, but you should force her to have quiet time in her room.
It sounds like she is still in a crib. I would continue to stay with her to get her to nap until you switch her to a bed. Then, don't allow her to come out of her room. You will make it so much easier for her if she is used to "quiet time" once she gets to kindergarten.
Good luck!
Dawn