B.B.
My son stopped taking naps at home and at daycare just after he turned two when he was home with me. He still has quiet time for two hours during the afternoons when he is home with us on the weekends. We found it interesting that when he started Pre-K in September (he's 3 1/2 and goes to a full day Pre-K program the school district I work for has for teachers) that he actually is taking naps during the 90 minute "rest period" in the afternoons. He still isn't taking them on the weekends, but he does nap at school almost every day now.
I wouls still continue to put her down or have some sort of quiet time. It will allow for her to re-fuel for the rest of the day.