No! J.K. Rowling was writing as early as six years old! Christopher Paolini was just 15 years old when he began writing Eragon, the first book in the Inheritance trilogy. Jane Austen was a teenager when she wrote one of her novels.

There is no age limit to be an author. If you have a knack for story-telling, then it will be there automatically, and in most authors this is usually at an early age. Or, if they didn't write at an early age, then they certainly read a lot of books. There are some authors who don't attempt their first novel until they are older. Authors who have previously worked as editors may not attempt a novel until later years.

Obviously older authors may have more knowledge than children, so they will be able to produce more detailed work, but children who wish to write shouldn't be discouraged and should be left to follow what they wish to do.