If you'r being asked
-Где она?, you need to say
-Она пошла, but
Она was already said, it's clear that you talk about her, why you need to use that again?
If you'r being asked
In the example you gave, it is not strictly necessary to repeat Она. As you correctly pointed out, the previous sentence is already speaking of она, therefore it is clear what the conversation is about.
Как она тебе?
There is nothing wrong with using она for the second time, however in the examples above it would only make sentences sound worse, not better.
You are much more likely to actually need to use it where there's more than one (feminine or otherwise) subject (e.g. the она you're talking about plus somebody/something else). For example,
Где она сейчас, где ее мать?
Она - в Лондоне.
(This means, she is in London, but I am not saying anything about her mother. On the other hand, saying simply In London would mean that they both are in London.)
Где она со своим другом? (Note that a better usage would be где они.)
(She's gone, but I am not saying anything about her friend.)
If you answer the question with -Она пошла, you should specify where to, and that is obligatory. If you say 'она ушла', then the usage of the pronoun is arbitrary; that is, you don't always have to use it.
Strange enough, here I might agree with 'shabunc'; this being a partially duplicating question.
Just a side note, which, however, could still serve as an answer. The thing is "пошла" could as well be a verb in the imperative mood, that is, it could mean "Start walking!", "Go!", "Forward!", "Go forward!" when applied to a woman. So, if we imagine that the one who asked the question "Где она?" is a female, then the answer "Пошла" in this case would simply mean something like "Start walking and don't ask stupid questions!" or "Start walking, and no talking!" (of course, in the written speech "Пошла" would probably be written with an exclamation mark: "Пошла!"). So, to avoid that connotation, adding "Она" before "пошла" will make sure that the one who is answering is still speaking in the indicative mood, not in the imperative one, which means that he or she is still answering the question and not giving any commands.