Routing Protocol for Low-power Lossy Networks (RPL) is designed by Internet Engineering Task Force (IETF) as the de facto routing standard for Internet of Things (IoT). Supporting mobility and providing Quality of Service (QoS) in the timeliness domain were not addressed in the IETF standard. RPL performs poorly when it comes to satisfying QoS constraints and adaptability to changes in the network topology. In this paper, we address this formidable problem by proposing QCF, a QoS-aware Communication Framework for real-time IoT services. Our proposed framework provides a lightweight practical approach to support timeliness requirements, and node mobility. It applies fuzzy logic to balance energy resources and traffic loads in the network. QCF estimates node mobility and the one-hop delay by using two novel methods. It employs two-hop neighbor information to enhance the parent selection process, and estimates the remaining time to the packet’s deadline without using synchronized clocks. We integrate QCF into the Contiki operating system and implement it on Zolerita IoT motes. Emulation results show that QCF improves the deadline delivery ratio by up to 67% and reduces the end-to-end delay by up to 63%.