Magneto-active elastomers (MAEs) are advanced composite materials consisting of a soft elastomeric matrix embedded with magnetic micro-inclusions. These materials exhibit complex multiscale response that presents significant challenges for modeling and analysis. In the absence of an external magnetic field, the mechanical behavior of MAEs can be approximated as that of a rubber matrix reinforced with rigid filler particles. However, under an applied magnetic field, the magneto-mechanical coupling arises from magnetic interactions among the embedded particles. These interactions induce macroscopic deformations of the elastomer and lead to microstructural rearrangements, such as the formation of particle columns aligned with the field. To characterize the mechanical behavior, a transversely isotropic Neo-Hookean model is employed, capturing the anisotropic elastic response of the material. The magnetic behavior is modeled using a dipolar mean-field approach, which accounts for interactions between magnetized particles under an external field. Furthermore, an additional term is introduced governing the microstructural evolution caused by the application of a magnetic field. Several forms of this term are systematically evaluated to identify the most effective framework for capturing microstructural dynamics. The proposed model enhances our understanding of the interplay between microstructural evolution and the reinforcement of mechanical stiffness of the MAEs caused by the application of magnetic field, thereby providing critical insights into their behavior and guiding the development of predictive tools for these multifunctional materials.