Quoting s00nt0be04:" Can a 3 year old get insomnia? My daughter is usually the best one out of her and her siblings to be ... [snip!] ... and a half past bed time. My other 2 are knocked out. Ugh. Sorry if I misspelled or left something out. Posting from my phone."
It could just be that she's at the age where she's learning that she can control certain things, like when she falls asleep or how much she eats (my son used that one against me), and she's just pushing the boundaries. I wouldn't take away her books, though, I'd keep with the regular routine.