Underwater monitoring and surveillance involves the detection, classification, localisation and tracking of targets underwater. Typical approaches involve the use of dedicated sensor systems for detection, e.g. monostatic/multistatic sonar, passive acoustic sensors or visual/infrared cameras, and a separate communication system for the nodes to deliver the data to shore. In this paper, we consider an alternative way of detecting underwater targets-simultaneous underwater acoustic communication (UAC) and target detection using a network of underwater nodes, where regular data transmissions are "reused" for the purpose of target detection. In particular, this study focuses on the development of network protocols that can enable such networks to: 1) detect potential targets moving through water; 2) deliver the detection information reliably and with adequate latency to a master station on shore. To this end, we develop a solution based on Spatial Time Division Multiple Access (STDMA), robust multipath routing, and data aggregation at the relays. The simulation studies show that the STDMA-based Link layer provides a high probability of detection for targets moving at typical AUV speeds (up to 2 m/s), while the Gradient routing protocol combined with data aggregation at the network nodes provides a good trade-off between the end-to-end packet delivery ratio and latency, compared with Flooding and shortest path routing.