Energy harvesting is a promising technology for the Internet of Things (IoT) towards the goal of self-sustainability of the involved devices. However, the intermittent and unreliable nature of the harvested energy demands an intelligent management of devices' operation in order to ensure a sustained performance of the IoT application. In this work, we address the problem of maximizing the quality of the reported data under the constraints of energy harvesting, energy consumption and communication channel impairments. Specifically, we propose an energy-aware joint source-channel coding scheme that minimizes the expected data distortion, for realistic models of energy generation and of the energy spent by the device to process the data, when the communication is performed over a Rayleigh fading channel. The performance of the scheme is optimized by means of a Markov Decision Process framework.