"A divine designer is all but ruled out by the consideration that he must at least as complex as the entities he was wheeled out to explain."
Even as an atheist, I disagree with this statement. It is simple to "design" very simple, even trivial, systems—for example, cellular automata (Wolfram's NKS)—that have exceedingly complex behaviour. A designer could start a system in a simple state (such as the initial conditions for the big bang) and just let it evolve via a simple set of rules.
However, if Dawkins is defining the "designer" to be able to foresee all possible outcomes of his or her design then indeed the statement holds true (essentially the principle of Computational Irreducibility).
So the definition of "designer" is paramount here.