Clearly, $Q_{0}$ alternates in every clk cycle as $Q_{0}'$ is fed as input and it is D flipflop.
$Q_{1}$ becomes $1$ if its prev value and current $Q_{0}$ differs (EXOR).
So, the sequence of transitions will be $: 00 \rightarrow 11 \rightarrow 01 \rightarrow 10 \rightarrow 00$, (D) choice.