  Let $A$ be a simple, exact, separable, unital $C^*$-algebra and let $\alpha
\colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak
tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is
quasidiagonal provided that all traces on $A$ are quasidiagonal. As an
application, we study the behavior of finite decomposition rank under taking
crossed products by finite group actions with the weak tracial Rokhlin
property. Moreover, we discuss the stability of the property that all traces
are quasidiagonal under taking crossed products of finite group actions with
finite Rokhlin dimension with commuting towers.
