Have you tried to separate "reading to her" from "reading"?
Way back when I refused to learn how to read before starting 1st grade. One of the reasons was that I did *not* want my grandfather to stop reading books to me, an activity I treasured. When my children started learning how to read I completely separated our daily evening reading sessions from their school reading practices -- made easier by the fact that our home and school languages are different.
Maybe try telling your daughter that you love reading books to her and will never stop, and have her show off/practice her skills at a different time?
