We introduce WhaVax, a new expert-annotated dataset of vaccine-related WhatsApp messages collected from large Brazilian public groups spanning multiple pandemic years. The dataset was constructed through a rigorous, carefully designed pipeline that integrates keyword-based data collection, semantic deduplication to remove near-duplicate content, and a multi-stage annotation protocol conducted by medical specialists. This process produced a high-quality gold-standard corpus, characterized by substantial inter-annotator agreement and strong reliability for downstream analysis. Additionally, we provide a detailed characterization of WhatsApp misinformation, revealing distinctive linguistic, structural, lexical, temporal, and group-level patterns, as well as a meaningful layer of ambiguous cases that reflect the complexity of health discourse in private messaging. We also benchmark classical models, fine-tuned Small Language Models, and zero- or few-shot Large Language Models under realistic data-scarcity constraints, demonstrating that strong embeddings and LLM approaches perform competitively, while domain alignment and data availability remain critical factors. This study provides a rare, high-quality resource to support misinformation research and computational modeling in encrypted communication environments.