Do they cut a girls hair for basic?

No, they do not typically cut women's hair in the military. I say "typically" because your hair must be within military regulations. Look up AR 670-1. Your hair may not be styled in a "faddish" way, and must be a single natural color. When you wear your uniform, your hair may not touch the collar. You may put it in a bun, but this cannot interfere with wearing military headwear. Other than that, there is no length requirement.

only the Navy requires it.

the rest of the branches will only do so if you cannot maintain standards.

as long as it meets the regulations, you should be fine. my TI used to say (and to a point, i agree) that "Equality starts at the barber's chair"

might cut down on the sexual harassment in the military if everyone got a buzz cut... frankly with the military's relaxed policy toward h0m0sexuals, i am waiting for some weenie of a man to try to file a suit saying "i should not get a buzz cut because that is sex discrimination"....