It's kindergarten. Stop worrying about her being challenged. The new social aspect will be challenging enough.

Also, if your child has never been to school, has her reading level been evaluated by some other assessment outside of school? How did you come to the reading level at 4th-5th grade? There is more to reading than knowing the words. Comprehending the reading material is more important than knowing the words.

When mine was in kindergarten, they also had weekly spelling tests. They weren't taught to spell phonetically, they were taught to spell correctly. And they went into first grade being expected to spell words correctly. This is a small public school district in rural US. If your daughter is only just learning to spell words phonetically, then she could be behind if she skips kindergarten. If your district is similar to ours that is.

Also, if you're in the US, I would avoid teaching her any math at home at all. Math these days is being taught much differently than when we were kids, especially if your district teaches Common Core. Teaching her challenging math concepts at home independently could actually confuse her much more and put her behind at school.