Flood models inform strategic disaster management by simulating the spatiotemporal hydrodynamics of flooding. While physics-based numerical flood models are accurate, their substantial computational cost limits their use in operational settings where rapid predictions are essential. Models designed with graph neural networks (GNNs) provide both speed and accuracy while having the ability to process unstructured spatial domains. Given its flexible input and architecture, GNNs can be leveraged alongside physics-informed techniques with ease, significantly improving interpretability and generalizability. We introduce a novel flood GNN architecture, DUALFloodGNN, which embeds physical constraints at both global and local scales through explicit loss terms. The model jointly predicts water volume at nodes and flow along edges through a shared message-passing framework. To improve performance for autoregressive inference, model training is conducted with a multi-step loss enhanced with dynamic curriculum learning. Compared with standard GNN architectures and state-of-the-art GNN flood models, DUALFloodGNN achieves substantial improvements in predicting multiple hydrologic variables (e.g., water volume, flow, and depth) while maintaining high computational efficiency. The model is open sourced at https://github.com/acostacos/dual_flood_gnn. The dataset is open sourced at https://hdl.handle.net/2123/35293 with the DOI 10.25910/9xav-0s86.