hi and welcome
my rosie had that and was given a injection and some antibiotocs the vet did a skin scrap and said it was a mite that she was born with, she also played alot and still ate well, now the mite has gone her fur is growing back lovely and thick (and she needs that in the uk).
so if i was you id ask your vet for a skin scrap then if it isnt that it can be ruled out. keep us informed. by the way she is a cutie
wendy and rosie