Unmanned Aerial Vehicles (drones) are emerging as a promising technology for both environmental and infrastructure monitoring, with broad use in a plethora of applications. Many such applications require the use of computer vision algorithms in order to analyse the information captured from an on-board camera. Such applications include detecting vehicles for emergency response and traffic monitoring. This paper therefore, explores the trade-offs involved in the development of a single-shot object detector based on deep convolutional neural networks (CNNs) that can enable UAVs to perform vehicle detection under a resource constrained environment such as in a UAV. The paper presents a holistic approach for designing such systems; the data collection and training stages, the CNN architecture, and the optimizations necessary to efficiently map such a CNN on a lightweight embedded processing platform suitable for deployment on UAVs. Through the analysis we propose a CNN architecture that is capable of detecting vehicles from aerial UAV images and can operate between 5-18 frames-per-second for a variety of platforms with an overall accuracy of ~ 95%. Overall, the proposed architecture is suitable for UAV applications, utilizing low-power embedded processors that can be deployed on commercial UAVs.