Quantum illumination is a quantum optical sensing technique, which employs an entangled source to detect low-reflectivity object immersed in a bright thermal background. Hybrid cavity-optomagnonics system promises to work as quantum illumination because a yttrium iron garnet (YIG) sphere can couple to microwave field and optical field. In this paper, we propose a scheme to enhance the entanglement between the output fields of the microwave and optical cavities by considering the intrinsic Kerr nonlinearity of the YIG. We investigate the difference between intrinsic Kerr nonlinearity and optomagnonical parametric-type coupling on improving entanglement. Our result show that the large value optomagnonical parametric-type coupling does not mean the large entanglement, nevertheless, the large value of Kerr nonlinearity does monotonously improve the entanglement for our group of parameters. Consequently, under feasible parameters of current experiment, the signal-to-noise ratio and probability of detection error can be improved after considering the magnon Kerr nonlinearity.