The routing protocol for low power and lossy network (RPL), constructed according to the objective function (OF), is the standard for routing selection in low power and lossy networks (LLNs). Most schemes utilise the expected transmission count (ETX) as the routing metric for the next hop. Designing effective and efficient routing protocols in LLNs require the mechanism to meet the criteria of different applications or services. In this paper, we propose a service-aware OF with quality of service (SOF-QoS) mechanism which integrates received signal strength indicator (RSSI), energy consumption, and hop count metrics into RPL OF for path selection according to different services, such as normal data, video packets and emergency messages transmission in LLNs. The proposed SOF-QoS mechanism defines various weights with fuzzy logic for the next routing selection in response to each service. We conduct the simulation under different network topologies with static and mobile scenarios to analyse the performance of the proposed SOF-QoS mechanism and compare them with the traditional RPL schemes. The simulation result shows that our proposed SOF-QoS mechanism provides relatively better or superior performance with reliability than traditional ones for different services.