The Artificial Intelligence Act of the European Union mandates that providers and deployers of high-risk AI systems establish a quality management system (QMS). Among other criteria, a QMS shall help to i) identify, analyze, evaluate, and mitigate risks, ii) ensure evidence of compliance with training, validation, and testing data, and iii) verify and document the AI system design and quality. Current research mainly addresses conceptual considerations and framework designs for AI risk assessment and auditing processes. However, it often overlooks practical tools that actively involve and support humans in checking and documenting high-risk or general-purpose AI systems. This paper addresses this gap by proposing requirements derived from legal regulations and a generic design and architecture of a QMS for AI systems verification and documentation. A first version of a prototype QMS is implemented, integrating LLMs as examples of AI systems and focusing on an integrated risk management sub-service. The prototype is evaluated on i) a user story-based qualitative requirements assessment using potential stakeholder scenarios and ii) a technical assessment of the required GPU storage and performance.