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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.
Many published authors are able to complete two or three books a year with only a few pages a day. Second, build up your page count slowly. If you're determined to get serious about your writing and you're going to give it more time, that's great. But don't try to jump from three pages a day to fifteen.