Recently powerful Large Language Models (LLMs) have become easily accessible to hundreds of millions of users world-wide. However, their strong capabilities and vast world knowledge do not come without associated privacy risks. In this work, we focus on the emerging privacy threat LLMs pose – the ability to accurately infer personal information from online texts. Despite the growing importance of LLM-based author profiling, research in this area has been hampered by a lack of suitable public datasets, largely due to ethical and privacy concerns associated with real personal data. We take two steps to address this problem: (i) we construct a simulation framework for the popular social media platform Reddit using LLM agents seeded with synthetic personal profiles; (ii) using this framework, we generate SynthPAI, a diverse synthetic dataset of over 7800 comments manually labeled for personal attributes.