Don't change your rate.
If she doesn't like it she can go elsewhere.
Just think about bundling up all the kiddos, possibly waking them from their nap to go and get this kid. What about in the miserable weather? Reallllllly think about that.
That is exactly why I don't do school age kiddos. Once my current group goes to school if they are still here than I may do it but until then no thanks.
Good luck and remember that this is YOUR business YOUR rules.