Vehicle to Vehicle (V2V) communication opens a new way to make vehicles directly communicate with each other, providing faster responses for time-sensitive tasks than cellular networks. Effective V2V routing protocols are essential yet challenging, as the high dynamic road environment makes communication easy to break. Many prediction methods proposed in the existing protocols to address this issue are either flawed or have a poor effect. In this paper, to cope with the two aspects of the problems that cause communication interrupt, i.e., link breaks and route quality degradation, we design an acceleration-based trajectory prediction algorithm to estimate the link lifetime, and a machine learning model to predict route quality. Based on the prediction algorithms, we propose PQR, a Prediction-supported Quality-aware Routing protocol, which can proactively switch to a better route before the current link breaks or the route quality degrades. Especially, considering the limitations of the current routing protocols, we elaborate a new hybrid routing protocol that integrates the topology-based method and location-based method to achieve instant communication. Simulation results show that PQR outperforms the existing protocols in Packet Delivery Ratio (PDR), Roundtrip Time (RTT), and Normalized Routing Overhead (NRO). Specifically, we have also implemented a vehicular testbed to demonstrate PQR's real-world performance, and results show that PQR achieves almost no packet loss with latency less than 10ms during route handoff for topology change.