Global quantum secure communication can be achieved using quantum key distribution (QKD) with orbiting satellites. Established techniques use attenuated lasers as weak coherent pulse (WCP) sources, with so-called decoy-state protocols, to generate the required single-photon-level pulses. While such approaches are elegant, they come at the expense of attainable final key due to inherent multi-photon emission, thereby constraining secure key generation over the high-loss, noisy channels expected for satellite transmissions. In this work we improve on this limitation by using true single-photon pulses generated from a semiconductor quantum dot (QD) embedded in a nanowire, possessing low multi-photon emission ($<10^{-6}$) and an extraction system efficiency of -15 dB (or 3.1%). Despite the limited efficiency, the key generated by the QD source is greater than that generated by a WCP source under identical repetition rate and link conditions representative of a satellite pass. We predict that with realistic improvements of the QD extraction efficiency to -4.0 dB (or 40%), the quantum-dot QKD protocol outperforms WCP-decoy-state QKD by almost an order of magnitude. Consequently, a QD source could allow generation of a secure key in conditions where a WCP source would simply fail, such as in the case of high channel losses. Our demonstration is the first specific use case that shows a clear benefit for QD-based single-photon sources in secure quantum communication, and has the potential to enhance the viability and efficiency of satellite-based QKD networks.