A robot planning under uncertainty must trade goal progress against whether it will be able to localize itself effectively at potential future positions. We study this problem in Gazebo simulation for a mobile robot localized by a fixed external camera, where detector reliability varies with viewpoint, occlusion, and image-space effects. The controller maintains a Gaussian pose belief. A global finite-horizon Expected Free Energy route solve optimizes a bounded unicycle-command sequence, and a local tracker follows the resulting waypoints. We introduce a detector-score-derived covariance model obtained by fitting a Gaussian process to raw scores from a trained object detector. The Gaussian process prediction is mapped to an effective image-space observation covariance, so expected measurement uncertainty enters the predicted observation distribution and belief propagation. In the tested route-choice tasks, the learned-covariance planner more often selected camera-observable routes, showed lower planar localization error in the representative paired run, and achieved more goal completions with fewer collisions than the constant-covariance baseline. These results provide preliminary evidence that state-dependent camera-update covariance can improve belief-aware route selection under external-camera observations.