Small superfical cuts that do not gape do not need stitches (just like skin cuts).
JCH MD
It must be just the top layer that is cut. The eye moves fine and she is not in pain. Thank yo.
The sclera is the white of the eye and if that was indeed split it would be a dire emergency. More likely the conjunctiva overlying the sclera and the tenon fascia underneath are what was cut. If the edges are gaping, there is severe pain, or the eye does not move properly then you will need to have the child seen by an Eye MD or in the ER.
JCH MD