Hybrid Quantum Neural Networks (HQNNs) have recently emerged as a promising paradigm for near-term quantum machine learning. However, their practical performance strongly depends on design choices such as classical-to-quantum data encoding, quantum circuit architecture, measurement strategy and shots. In this paper, we present a comprehensive design space exploration of HQNNs for Chronic Kidney Disease (CKD) diagnosis. Using a carefully curated and preprocessed clinical dataset, we benchmark 625 different HQNN models obtained by combining five encoding schemes, five entanglement architectures, five measurement strategies, and five different shot settings. To ensure fair and robust evaluation, all models are trained using 10-fold stratified cross-validation and assessed on a test set using a comprehensive set of metrics, including accuracy, area under the curve (AUC), F1-score, and a composite performance score. Our results reveal strong and non-trivial interactions between encoding choices and circuit architectures, showing that high performance does not necessarily require large parameter counts or complex circuits. In particular, we find that compact architectures combined with appropriate encodings (e.g., IQP with Ring entanglement) can achieve the best trade-off between accuracy, robustness, and efficiency. Beyond absolute performance analysis, we also provide actionable insights into how different design dimensions influence learning behavior in HQNNs.