Dd2 was the same, and has always been in mainstream. Don't overthink it, really. You need do nothing different - she's a perfectly ordinary child. She can just read - she hasn't got two heads or anything.
You don't need to 'do' anything. You don't need to change nursery, or look for indie schools, or anything.
Honestly. Just let her be a kid, and let her read. It's fine.
Dd2 didn't read at nursery. Nursery isn't for reading. It's for learning social skills, having fun with friends, and developing fine motor skills leading to writing. Not for reading. Payouts can continue to read her stories, she can read herself at home. No need to attempt to shoe horn this into nursery as well. She can get enough reading at home. It would be very boring to read at nursery, and completely unnecessary.
School? Schools just start at yr r. At the very least they go up to yr 2, which means they all have an adequate supply of decent chapter books under their roves that are available to all pupils. She will just get them from the yr 2 shelf (or up to y6 of it is a primary school). Here are a ton of books in every school, for all levels of readers. Your kid will find a ton of books to read.
Reading early is not a problem. It is no big deal. Honestly. Dd2 could pretty much read everything before she started school, and I can honestly say that she has never been bored as a result of this skill - in actuality, it stopped her being bored, because she could always sit and read a book.
Relax. Let her read. Let life carry on. Perfectly normal, and no need to panic. Nobody died. 