If your daughter wants a flute for LARPing I recommend a treble recorder, since they were cheaper and so more widely used in times of old.
They are built as Basso (F), Tenore (C), Alto (F), Soprano (C), Sopranino (F) and The Very Small Recorder (C). With small hands she is predestined for Soprano and the smaller ones.
I played The Very Small Recorder once (about 1 1/2 fingers long), but my fingertips grew too thick.
The trebles have two ways of grips: the Baroque are played with forked grips, and the German not (easier to play, but not so pure in some sounds).
I only know German fabricants; I prefer Mollenhauer of Fulda.

Wilfried