I think 1st grade has changed quite a bit in 30 years, but I do not think that your child will have a peer group at her level, from what you are describing. Maybe there will be one other child.
In our district, Kindergarten has the academics that I remember from my own 1st grade. So, yes, many children can read at a basic level entering 1st, and a few will be reading easy chapter books. However, the spelling lists, even the challenge lists, were incredibly simple and most of the time was spent teaching very basic reading and math skills.
I agree with looking at the school website and looking at the class materials available there.
