she will think that she is expected to do the same
Sadly she is expected to do the same. This is the problem - as you say, we don't see the full range of hairless - hairy women because almost without exception, we remove our body hair... because we are expected to and because, like it or not, it isn't 'acceptable' to go around with hairy legs and pits - we may be able to 'get away with it' in informal situations, or just wandering about town, (and I applaud you for doing so) - but what about work? What about if you were on a date? Would you honestly feel able to go hairy in these situations? FWIW, I did used to go around hairy a lot more when I was younger - it's possible to do so and be taken as 'alternative' or bucking the trend or whatever. Now I've hit my 40's it doesn't feel so easy because the perception is just that I've 'let myself go'.
I do not see how I can bring her up aware of the patriarchal and sexualising nature of our society and then at 13 hand her a razor and say, 'its not you, its society but you'd better sort yourself out cause otherwise you'll be bullied'. That seems ludicrous.
It's not a question of telling her she'd 'better sort herself out' - what would you do if you noticed your DD wearing thick tights in the middle of summer, obviously uncomfortable, and you asked her why and she told you it's because her legs are hairy and she's already being teased?