This POR is possible and enphasizes her request, but it is not necessary and can rarely be heard in everyday speech. Prefer:
A menina pede água.
"A menina pede água", and not "pede por água". this sounds like a bad translation from English.
i am not native portuguese speaker, but i am native spanish speaker, and in spanish i would say "La niña pide água" wich would traduce "A menina pede água" in portuguese, but i am not sure if it's the same in portuguese