Autonomous underwater robotic systems offer scalable and cost-effective solutions for ocean observing; however, their development remains constrained by the high risk and expense of field-based testing. Digital twin (DT) technologies address this challenge by enabling realistic pre-deployment simulation and validation, reducing reliance on costly in-water trials while supporting safer and more efficient deployment of autonomous systems in marine operations. This research presents a physics-based DT for a small-scale remotely operated vehicle (ROV), targeting ocean observing applications such as reef monitoring and subsea surveys. The proposed DT integrates geometric and inertial data derived from a 3D CAD model with key hydrodynamic effects, including drag, added mass, and buoyancy, to approximate six-degree-of-freedom underwater dynamics within a closed-loop simulation environment. Autonomous behaviours relevant to real-world marine operations, including station-keeping, waypoint following, and vision-based object tracking, are demonstrated. The vision-based task provides a quantifiable benchmark for perception performance in biologically relevant observation scenarios. Validation is demonstrated by comparing simulation outputs with controlled physical experiments across key metrics, including positional accuracy, stability, and response time. This work demonstrates how DT methodologies can reduce development risk and cost while enabling scalable and repeatable deployment of autonomous underwater systems, contributing to more efficient and reliable ocean observing operations.