Let $g\in H(\Bbb D)$, $n$ be a nonnegative integer and $\varphi$ be an analytic self-map of $\Bbb D$. We study the boundedness and compactness of the integral operator $C_{\varphi,g}^n$, which is defined by $$ (C_{\varphi,g}^nf)(z)=\int_0^zf^{(n)}(\varphi(\xi))g(\xi)d\xi,\quad z\in\Bbb D,\quad f\in H(\Bbb D), $$ from $Q_K(p,q)$ and $Q_{K,0}(p,q)$ spaces to $\alpha$-Bloch spaces and little $\alpha$-Bloch spaces.