Advances in robotics have allowed mobile robotic platforms to be deployed in an increased number of field operations. The dynamic nature of the operating environment can constrain the robotic mission execution in terms of required time or energy. Current solutions for providing optimal and optimized plans for the resource-constrained sensing mission planning only consider holonomic vehicles. This letter proposes the Dubins Correlated Orienteering Problem (DCOP) as a solution for resource constrained sensing missions undertaken by a nonholonomic Dubins vehicle. It provides a Genetic Algorithm heuristic for finding optimised solutions in a timely manner. The proposed heuristic is compared against the GA heuristic solution for the Correlated Orienteering Problem (COP) and the heuristic for the Dubins Orienteering Problem (DOP). It performs equally good with the COP heuristic in terms of utility with an increase in the execution time. When tested against the DOP problem it performs comparably good. In the worst case, it produces solutions with 13% less utility but requiring orders of magnitude less time than the state of the art. Finally, the proposed method is tested in a scenario where the budget consumption is changing during mission execution. It is shown that a new plan can be devised online, leading to increased mission performance. Given the results, it sets the baseline for comparing any future approaches that will address the DCOP problem.