Let $\varphi$ be an analytic self-map of the open unit disk $D$ on the complex plane and $\alpha>0$, $p\geq 0$, $n\in\Bbb N$. In this paper, the boundedness and compactness of the products of composition operators and $n$th differentiation operators $C_\varphi D^n$ from $\alpha$-Bloch space $B^\alpha$ and $B^\alpha _0$ to $Q_p$ space are investigated.