High-quality personalized question banks are crucial for supporting adaptive learning and individualized assessment. Manually designing questions is time-consuming and often fails to meet diverse learning needs, making automated question generation a crucial approach to reduce teachers' workload and improve the scalability of educational resources. However, most existing question generation methods rely on single-agent or rule-based pipelines, which still produce questions with unstable quality, limited diversity, and insufficient alignment with educational goals. To address these challenges, we propose EduAgentQG, a multi-agent collaborative framework for generating high-quality and diverse personalized questions. The framework consists of five specialized agents and operates through an iterative feedback loop: the Planner generates structured design plans and multiple question directions to enhance diversity; the Writer produces candidate questions based on the plan and optimizes their quality and diversity using feedback from the Solver and Educator; the Solver and Educator perform binary scoring across multiple evaluation dimensions and feed the evaluation results back to the Writer; the Checker conducts final verification, including answer correctness and clarity, ensuring alignment with educational goals. Through this multi-agent collaboration and iterative feedback loop, EduAgentQG generates questions that are both high-quality and diverse, while maintaining consistency with educational objectives. Experiments on two mathematics question datasets demonstrate that EduAgentQG outperforms existing single-agent and multi-agent methods in terms of question diversity, goal consistency, and overall quality.