This is your best bet, but it may not work. Often women feel the need to give something personal and prove to themselves they are brave and not vain. It's symbolic more than anything. Some - and of course I can't speak for your girlfriend specifically - enjoy the martyr-like attention they get for the sacrifice.

She may also want to cut her hair, and this is just an excuse to do it without getting flak.

If she seems set on it, you might want to have your fun while you can. If she seems uncertain or if there's another friend pressuring her, then you might have a chance to save her mane by telling her how much you like it.