That is a unique issue. My daughter began having the same issue though a tad older. While it wasn't severe, it was certainly noticeable.
I resolved the issue by using a natural deodorant (one without the aluminum based antiperspirant); it seems to work well. I use "Kiss My Face" Lavender scented. The deodorant does not irritate her sensitive skin and doesn't prevent healthy sweating either. You may get this or another recommendation from your local health food store.
I hope this is helpful. BTW, I just looked at the dietary advice and I think this is all useful stuff. Diet was not an issue with my daughter. We don't eat much red meat and try to get free range or hormone free meat; she also is not a big milk drinker. And she is 10 now and no signs of body hair (thank goodness).