The Princess and the Moon(1983)

Otsuki-sama to Oujo

Sachiko is an unhappy girl who is very picky about food, which is why she doesn't get enough energy and performs poorly at school PE classes. One night, a white rabbit appears and takes her to the Land of the Moon. There, she meets a princess who looks exactly like her except that she is active, happy and healthy. This meeting inspires Sachiko to change her ways.