I will never look to others to find my happiness. You don't have to want to be Miss USA or even be interested in pageants for that matter. You just have to have a will to better yourself and make things happen for you.
I think rather than feeling persecuted that you're meeting up with a challenge simply because of the gender you belong to, I think it's important to face the challenge for what it is and have your convictions together.
I would tell her to believe in herself because it is not only physical beauty that is important but also inner beauty. Just like what the Little Prince said, the essential things are invisible to the naked eye. (On giving advice to girls with low self esteem)