Magnetic topological materials, which combine non-trivial band topology with intrinsic magnetism, have emerged as a promising platform for low-power spintronics. In this work, we systematically investigate the structural stability, magnetic ground state, electronic structure, and topological properties of a Ti-doped LiMgP monolayer by using first-principles calculations within the density functional theory (DFT) framework. The calculated binding energy (E_b) and formation energy (E_f) indicate excellent structural stability and suggest the experimental feasibility of synthesizing this material. Phonon dispersion and ab initio molecular dynamics (AIMD) simulations at different temperatures further demonstrate the outstanding dynamical and thermodynamic stability of the system. A thorough analysis of the magnetic mechanism reveals that the Ti atoms exist in the form of a Ti²⁺ valence state at the center of a planar triangle crystal field generated by the surrounding P^3- ligands. Driven by Hund's rule, the two 3d electrons occupy parallel spin states in the spin-up channel, giving rise to local magnetic moments that align ferromagnetically through exchange interactions. Monte Carlo (MC) simulations based on the extracted Heisenberg exchange parameters yield a ferromagnetic ground state with a Curie temperature (TC) of 97 K. In the absence of spin-orbit coupling (SOC), the monolayer behaves as a fully spin-polarized (100%) ferromagnetic Weyl semimetal. Upon including SOC, a global band gap opens, gapping out the Weyl points, driving a topological phase transition to a magnetic topological insulator and giving rise to the quantum anomalous Hall effect (QAHE) with a Chern number of C = +1. Furthermore, the pronounced Berry curvature near the Fermi level (E_F) produces a significant anomalous Nernst effect (ANE), with the anomalous Nernst coefficient reaching up to 1.54 A/(m·K), which substantially exceeds that of conventional thermoelectric materials. These findings establish the Ti-doped LiMgP monolayer as an SOC-driven magnetic topological material that uniquely integrates ferromagnetic half-metallicity, topologically non-trivial band structure, and large Berry curvature responses, positioning it as an ideal platform for exploring both low-power spintronic devices and efficient transverse thermoelectric conversion.