I think Doctor Who is a children's show in the same sense that the Narnia stories are for children, or the Alice books, or the majority of the traditional story tales. Namely, it is possible to thoroughly enjoy them at that level, but the (better) stories simultaneously deal with much deeper material that is truly adult. To take Narnia as an example, for a change, in "The Last Battle" there is a paragraph explaining the difference between Aslan and Tash which is so simply written a child can understand it, but is also conceptually very sophisticated. And if you don't know the reference: now's the time to read the book!