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It's okay to publish a book at any age. If it is a good book (or at least good enough.) Worse come to worse, if you can't publish at age 13, you can try again at age 18 or age 23. A famous writer, Pearl S. Buck published her first book at age 10, I believe.
Here we have novels for children aged from seven to 12, and there are two sections here: the seven to nine books, and the nine to 12 category, which is a core area of children's publishing. Obviously books at the younger end tend to be shorter: 15,000-20,000 words, say (though there aren't any rules).