Federated learning (FL) can empower Internet-of-Vehicles (IoV) networks by leveraging smart vehicles (SVs) to participate in the learning process with minimum data exchanges and privacy disclosure. The collected data and learned knowledge can help the vehicular service provider (VSP) improve the global model accuracy, e.g., for road safety as well as better profits for both VSP and participating SVs. Nonetheless, there exist major challenges when implementing the FL in IoV networks, such as dynamic activities and diverse quality-of-information (QoI) from a large number of SVs, VSPs limited payment budget, and profit competition among SVs. In this paper, we propose a novel dynamic FL-based economic framework for an IoV network to address these challenges. Specifically, the VSP first implements an SV selection method to determine a set of the best SVs for the FL process according to the significance of their current locations and information history at each learning round. Then, each selected SV can collect on-road information and offer a payment contract to the VSP based on its collected QoI. For that, we develop a multi-principal one-agent contract-based policy to maximize the profits of the VSP and learning SVs under the VSPs limited payment budget and asymmetric information between the VSP and SVs. Through experimental results using real-world on-road datasets, we show that our framework can converge 57% faster (even with only 10% of active SVs in the network) and obtain much higher social welfare of the network (up to 27.2 times) compared with those of other baseline FL methods.