Real-world optimization often demands diverse, high-quality solutions. Quality-Diversity (QD) optimization is a multifaceted approach in evolutionary algorithms that aims to generate a set of solutions that are both high-performing and diverse. QD algorithms have been successfully applied across various domains, providing robust solutions by exploring diverse behavioral niches. However, their application has primarily focused on static problems, with limited exploration in the context of dynamic combinatorial optimization problems. Furthermore, the theoretical understanding of QD algorithms remains underdeveloped, particularly when applied to learning heuristics instead of directly learning solutions in complex and dynamic combinatorial optimization domains, which introduces additional challenges. This paper introduces a novel QD framework for dynamic scheduling problems. We propose a map-building strategy that visualizes the solution space by linking heuristic genotypes to their behaviors, enabling their representation on a QD map. This map facilitates the discovery and maintenance of diverse scheduling heuristics. Additionally, we conduct experiments on both fixed and dynamically changing training instances to demonstrate how the map evolves and how the distribution of solutions unfolds over time. We also discuss potential future research directions that could enhance the learning process and broaden the applicability of QD algorithms to dynamic combinatorial optimization challenges.