Machine learning-based data rate prediction is one of the key drivers for anticipatory mobile networking with applications such as dynamic Radio Access Technology (RAT) selection, opportunistic data transfer, and predictive caching. User Equipment (UE)-based prediction approaches that rely on passive measurements of network quality indicators have successfully been applied to forecast the throughput of vehicular data transmissions. However, the achievable prediction accuracy is limited as the UE is unaware of the current network load. To overcome this issue, we propose a cooperative data rate prediction approach which brings together knowledge from the client and network domains. In a real world proof-of-concept evaluation, we utilize the Software Defined Radio (SDR)-based control channel sniffer FALCON in order to mimic the behavior of a possible network-assisted information provisioning within future 6G networks. The results show that the proposed cooperative prediction approach is able to reduce the average prediction error by up to 30%. With respect to the ongoing standardization efforts regarding the implementation of intelligence for network management, we argue that future 6G networks should go beyond network-focused approaches and actively provide load information to the UEs in order to fuel pervasive machine learning and catalyze UE-based network optimization techniques.