Woah, body hair sure has caused quite a stir!
Well, to answer the OP... this is what I'd do:
Teach your child to be a critical consumer of ideas. Apply critical thinking to the messages in songs, commercials, books, etc. Ask questions about what our culture promotes as beauty and why. How have these ideas evolved? Look at what is considered beautiful in other cultures or in other times (women with beards tattooed on, plates pierced through their lips, feet bound, necks stretched).
Teach your child to love herself, including her body. Research why hair grows where it does at different times in our life. Celebrate her budding body hair: "Is that peach fuzz getting thicker on your legs? You're becoming a woman! Let's talk about the other changes going on in your body..."
Don't be a hypocrite. If you're preaching about leg hair while you're dying your grey hair, your child will pick up on it.
And after all that, don't be surprised if she wants to shave at puberty. If so, let her. Don't make her feel guilty for being insecure (if she's motivated by peer pressure), it wont help her or you. It is age appropriate for teens to try on different roles and personas then discard them. Allowing her to try out "girlie" girl may just show her how uncomfortable, expensive, time consuming, and unnatural the process is.
While our culture provides conflicting and often harmful messages to women about more than just beauty, you are here asking this question which means you're proactively seeking to teach her something better. From one hairy mama to another: Lighten up. The good thing (or bad depending on how you feel) about body hair is that it will grow back.
Recipe for great deodorant that still allows you to sweat:
Sprinkle about 1/8 tsp of baking soda into your hand. Add a few drops of water to liquify. Rub under arms. Simple, Cheap, and works on hairy underarms too!