Distributed Acoustic Sensing (DAS) is a novel vibration sensing technology that can be employed to detect vehicles and to analyse traffic flows using existing telecommunication cables. DAS therefore has great potential in future "smart city" developments, such as real-time traffic incident detection. Though previous studies have considered vehicle detection under relatively light traffic conditions, in order for DAS to be a feasible technology in real-world scenarios, detection algorithms need to also perform robustly under heavy traffic conditions. In this study we investigate the potential of roadside DAS for the simultaneous detection and characterisation of the velocity of individual vehicles. To improve the temporal resolution and detection accuracy, we propose a self-supervised Deep Learning approach that deconvolves the characteristic car impulse response from the DAS data, which we refer to as a Deconvolution Auto-Encoder (DAE). We show that deconvolution of the DAS data with our DAE leads to better temporal resolution and detection performance than the original (non-deconvolved) data. We subsequently apply our DAE to a 24-hour traffic cycle, demonstrating the feasibility of our proposed method to process large volumes of DAS data, potentially in near-real time.