This paper introduces a novel channel knowledge map (CKM)-assisted dual-domain tracking and predictive beamforming scheme for high-mobility wireless networks. The central premise is that the CKM integrates both the coordinate and beam domains, thereby enabling tracking in one domain via treating the other domain's input as priors or measurements. In the coordinate domain (C-Domain), an extended Kalman filter (EKF) is employed to predict and track the state (i.e., location and velocity) of a moving communication receiver across time slots under both line-of-sight (LoS)-present and LoS-absent conditions, where the CKM provides a prior mapping from multipath channel parameters to potential target locations. In the beam domain (B-Domain), the updated location of the receiver is fed back to CKM to offer a priori information of angle of arrival (AoA) variations, which are incorporated to establish beam transition models for effective beam tracking, depending on the angular variation situation of each path. Then, we analyze the Cramér-Rao Bound (CRB) for AoA estimation for each path in the considered system and propose a jointly predictive beamforming and power allocation design to minimize AoA estimation errors, directly enhancing multipath beam tracking accuracy and indirectly improving target tracking performance. Simulation results demonstrate that the proposed scheme achieves significant improvements in both target and beam tracking performance compared to the state-of-the-art approaches, particularly in AoA tracking of non-line-of-sight (NLoS) paths, highlighting the potential gain of CKM in facilitating both target and beam tracking in high-mobility communications.