I use to be a preschool teacher and if your daughter is able to do all of what you say, then I suggest you continue to teach her at home as well as put her in school! Make sure you acknowledge her learning abilities so they are able to do other creative lessons with that do not make her bored.
My son is 3 years old. He can read some but he too has learned simple addition and counting to 110. Knows the days of the week, months of the year, and sign language. I am working on my second degree in Communication Disorders so I teach him a lot of the sign language that I have taken in college. He will be attending VPK this year but i will continue to teach him at home as well. I will def. be checking in with the teachers on updates with him to make sure he is not bored in the class in case I need to switch his pace.
I also teacher kids 2,3 and 4 online- check us out!
https://www.facebook.com/EarlyLearnersOnline