QoS forecasting for cellular vehicular communications allows cooperative, connected and automated mobility applications to tailor their behavior to the expected communication conditions on the road. In a nutshell, vehicles may, for example, execute cooperative maneuvers if the communication quality of service is only above a certain quantitative level whereas if not they revert to the individual autonomous mode. In this paper, we propose and show empirical methods for estimating packet-based QoS metrics obtained from 5G network measurements with a direct application to vehicular applications. As many distributed vehicular applications possess strict QoS requirements, we focus here on bounding packet-based statistical QoS quantiles, specifically for latency and loss. Our approach is based on training regression neural networks in a federated learning fashion and show that it can obtain predictions on par with centralized training without the vehicles needing to transmit raw measurement data. In contrast to QoS prediction using physical layer information, we briefly discuss the embedding of such much simpler application-level service within the 5G architecture. We also validate our approach through recovering classical closed-form delay quantiles that are obtained from analytical models of simple queueing systems. We show that our approach goes beyond these simple models in that it provides quantile estimates for the complex scenario of cellular vehicle communications and under different application traffic patterns including empirical data traffic traces as well as 5G testbed measurements.