The recently employed demand-response (DR) model enabled by the transformation of the traditional power grid to the SmartGrid (SG) allows energy providers to have a clearer understanding of the energy utilisation of each individual household within their administrative domain. Nonetheless, the rapid growth of IoT-based domestic appliances within each household in conjunction with the varying and hard-to-predict customer-specific energy requirements is regarded as a challenge with respect to accurately profiling and forecasting the day-to-day or week-to-week appliance-level power consumption demand. Such a forecast is considered essential in order to compose a granular and accurate aggregate-level power consumption forecast for a given household, identify faulty appliances, and assess potential security and resilience issues both from an end-user as well as from an energy provider perspective. Therefore, in this paper we investigate techniques that enable this and propose the applicability of Deep Neural Networks (DNNs) for short-term appliance-level power profiling and forecasting. We demonstrate their superiority over the past heavily used Support Vector Machines (SVMs) in terms of prediction accuracy and computational performance with experiments conducted over real appliance-level dataset gathered in four residential households.