My personal opinion: you should be over that by the time you are ten.
However, there is certainly nothing wrong with it when you are older. It just seems kind of sad to spend time writing to someone who will never personally read or respond to any of your correspondence. I just hope she realizes that any famous bands or singers all hire companies to take care of their fan mail and never actually read any of it.
Anyone would love to receive a fan letter from anyone from any age group. I don't believe we need to "grow out of" that kind of behavior. It's simply a gesture of kindness and adoration....all these performers need some positive feed-back just like the rest of us.
Fan letter writing at any age is a little silly. So with that in mind, I guess you're never too old for it. Most people just switch from fan letters to letters to the editor, that's all.