In mathematical psychology, recent models for human decision-making use Quantum Decision Theory to capture important human-centric features such as order effects and violation of the sure-thing principle (total probability law). We construct and analyze a human-sensor system where a quickest detector aims to detect a change in an underlying state by observing human decisions that are influenced by the state. Apart from providing an analytical framework for such human-sensor systems, we also analyze the structure of the quickest detection policy. We show that the quickest detection policy has a single threshold and the optimal cost incurred is lower bounded by that of the classical quickest detector. This indicates that intermediate human decisions strictly hinder detection performance. We also analyze the sensitivity of the quickest detection cost with respect to the quantum decision parameters of the human decision maker, revealing that the performance is robust to inaccurate knowledge of the decision-making process. Numerical results are provided which suggest that observing the decisions of more rational decision makers will improve the quickest detection performance. Finally, we illustrate a numerical implementation of this quickest detector in the context of the Prisoner's Dilemma problem, in which it has been observed that Quantum Decision Theory can uniquely model empirically tested violations of the sure-thing principle.