Yes, to the uninitiated it can seem a bit silly to question and parse out the meaning of ... "a better school" ... but it can be very important to understand what is meant by such phrases... as what is "better" for one is not necessarily "better" for all. There are lots of buzzwords... question, seek clarification, and delve into details.

Live and learn.

A few questions:

Where are her classmates from the first year of kindergarten... the children she was socially at ease with? Can you arrange for them to play together?

Have you checked State Laws and published school policies to see if they allow for acceleration under some circumstances?

Are there other possible educational options for your daughter?