Yes, most definitely. Little girls tend to not want to brush their hair, and will almost never leave it up in barrettes, therefore short hair is easy to care for.
Short haircuts are the more reasonable choice for some little girls especially those tender headed. Little girls should be able to wear their hair the way that suits them and their lifestyle the most. Everything should not always be based on appearance it should their way of living also.
I think that it depends on how short the haircut is. Also, to avoid embarrassment (for being possibly mistaken for boys), make sure that they have a bow.