humm does sound like Roseola ..I think you should ask the doctor as anti biotics may help her .Only other thing I came up with is a possibility of an allergy rash ...what does she have on the area of the rash regularly, any cream, lotion, even shower/bath gel ..and you say she has no rash anywhere else on her body ?
She has been getting sick (throwing up randomly) but no fever. She is very active. She eats very well, fruits and veggies every day. She doesn't seem to be bothered by the rash but it does worry me.
Am wondering if it could be Roseola ...how is she in herself has she been sick ,any fever?