Autonomous Vehicle (AV) perception systems have advanced rapidly in recent years, providing vehicles with the ability to accurately interpret their environment. Perception systems remain susceptible to errors caused by overly-confident predictions in the case of rare events or out-of-sample data. This study equips an autonomous vehicle with the ability to 'know when it is uncertain', using an uncertainty-aware image classifier as part of the AV software stack. Specifically, the study exploits the ability of Random-Set Neural Networks (RS-NNs) to explicitly quantify prediction uncertainty. Unlike traditional CNNs or Bayesian methods, RS-NNs predict belief functions over sets of classes, allowing the system to identify and signal uncertainty clearly in novel or ambiguous scenarios. The system is tested in a real-world autonomous racing vehicle software stack, with the RS-NN classifying the layout of the road ahead and providing the associated uncertainty of the prediction. Performance of the RS-NN under a range of road conditions is compared against traditional CNN and Bayesian neural networks, with the RS-NN achieving significantly higher accuracy and superior uncertainty calibration. This integration of RS-NNs into Robot Operating System (ROS)-based vehicle control pipeline demonstrates that predictive uncertainty can dynamically modulate vehicle speed, maintaining high-speed performance under confident predictions while proactively improving safety through speed reductions in uncertain scenarios. These results demonstrate the potential of uncertainty-aware neural networks - in particular RS-NNs - as a practical solution for safer and more robust autonomous driving.