Hair loss could be a severe side effect, doesn't mean it will happen to you....
The most common side effects seen in people taking Prozac include anxiety or nervousness, insomnia, drowsiness, headache, diarrhea, and rash. In addition, sexual side effects (reduced arousal or satisfaction) may occur. Prozac has also been shown to cause changes in appetite and weight, usually resulting in weight loss rather than weight gain.
Which is all normal for most anti-depressants but as it's said it's not permant.
When I even look up prozac side effects besides the obvious and even the more severe ones hair loss isn't one of them...
Who mentioned the hair loss bit to you?
I think it does occur it would have to be either extremely rare or a severe adverse reaction, though from even the severe rare symptoms hair loss is never mentioned.
I don't want to personally ever go on Prozac either really... there's only a selected few I'd ever consider taking...