I think deodorant is not about vanity at all and should be used the first time they start to smell like B.O. and not just a hot sweaty little kid. No matter what age that is.
As for shaving, I don't have a daughter but I know I would let her shave when it starts to hurt her confidence. Someone else asked this question a couple weeks ago and this is the answer I posted there.
I shaved at 11 but had thick dark hair and pale skin and wanted to shave sooner. I don't think that this isn't the same thing as makeup. It can definitely affect a girl's self esteem. And as far as giving in to peer pressure- Isn't that why we all shave? What other reason is there really for doing it? Yes, kids are too mature these days but that isn't their fault, and they shouldn't be "punished" for that fact. That is how I looked at it when I couldnt' shave and do things I wanted to, as a kind of punishment because HER mom wouldn't let her do it. Just because my mom did something at a certain time didn't mean it was relevant to my current situation. My mom was very odd about things like this sometimes, and really, it just made me feel like I couldn't come to her about concerns about my body. When she put her foot down on shaving and using acne facewash and no tampons, I felt like she would never listen to me about things like that, and so I stopped coming to her. I would rather have my daughter (if I ever have one) come to me and let me help her to find an appropriate solution for whatever her problem is, instead of going by the ads in magazines and articles that weren't necessarily appropriate. I certainly don't think parents should give in on any little thing to their kids, and this is definitely a good time to have conversations about self esteem. But I don't think encouraging self esteem requires withholding things like shaving to make them stronger. Just my two cents, I hope it helps.