She is still only little though, I don't know many kids her age that actually do that.
My youngest DD does but it's more about her temperament and that she likes to sit next to me with her own story whilst I have my head in mine

Keep reading at bedtime, that's terrific. I bet if you picked up a book and offered to read it to her at ANY time of the day she would love it. Actually it's the only way I can get my two into bed - they can be running around screaming their heads off after dinner but as soon as I call out "choose your stories" they are on the couch in a flash....