L.T.
We switched my son to a toddler bed at age 3. He is now 3 1/2. Since the switch he does not take regular naps. I insist he have some down time during the day so we put him in his room but he often gets up to play. He has some books and quiet toys in his room. I've decided as long as he is playing quietly I'm fine with that. Many days he does well without a nap. However, he will get tired and cranky about an hour before his normal bedtime so we look for the cues and put him to bed earlier when necessary. We have a baby gate at his bedroom door so he stays in his bedroom.
Thinking back, I noticed he was napping less often before the switch to the bed. Your daughter may not need regular naps if her nighttime sleep is sufficient. Maybe you could alter her nighttime sleep and either get her up 30-60 minutes earlier or put her to bed 30-60 minutes later and see if that helps with naptime.