The concern of overconfident mispredictions under distributional shift demands extensive reliability research on Graph Neural Networks used in critical tasks in drug discovery. Here we first introduce CardioTox, a real-world benchmark on drug cardiotoxicity to facilitate such efforts. Our exploratory study shows overconfident mispredictions are often distant from training data. That leads us to develop distance-aware GNNs: GNN-SNGP. Through evaluation on CardioTox and three established benchmarks, we demonstrate GNN-SNGP's effectiveness in increasing distance-awareness, reducing overconfident mispredictions and making better calibrated predictions without sacrificing accuracy performance. Our ablation study further reveals the embeddings learned by GNN-SNGP improves distance-preservation over its base architecture and is one major factor for improvements.