Let $C$ be an alphabet, $\delta : A \to \mathcal P (C \times A)$ a transition system over the set of states $A$. Let $Q : C \to C$ be a total function. A symmetric relation $R \subseteq A \times A$ is a Q-bisimulation iff. $(x,y) \in R$ and $(a,x') \in \delta x$ implies that there is $y'\in A$ such that $(b,y')\in \delta x$, $(b =Qa)$ and $(x',y')\in R$.
Indeed, the question holds also in the more general case when $Q$ is not just a function but a relation, and the condition $b=Qa$ becomes $(a,b) \in Q$.