With the widespread use of IoT applications and the increasing trend in the number of connected smart devices, the concept of routing has become very challenging. In this regard, the IPv6 Routing Protocol for Low-power and Lossy Networks (PRL) was standardized to be adopted in IoT networks. Nevertheless, while mobile IoT domains have gained significant popularity in recent years, since RPL was fundamentally designed for stationary IoT applications, it could not well adjust with the dynamic fluctuations in mobile applications. While there have been a number of studies on tuning RPL for mobile IoT applications, but still there is a high demand for more efforts to reach a standard version of this protocol for such applications. Accordingly, in this survey, we try to conduct a precise and comprehensive experimental study on the impact of various mobility models on the performance of a mobility-aware RPL to help this process. In this regard, a complete and scrutinized survey of the mobility models has been presented to be able to fairly justify and compare the outcome results. A significant set of evaluations has been conducted via precise IoT simulation tools to monitor and compare the performance of the network and its IoT devices in mobile RPL-based IoT applications under the presence of different mobility models from different perspectives including power consumption, reliability, latency, and control packet overhead. This will pave the way for researchers in both academia and industry to be able to compare the impact of various mobility models on the functionality of RPL, and consequently to design and implement application-specific and even a standard version of this protocol, which is capable of being employed in mobile IoT applications.