We show a H\"ormander spectral multiplier theorem for $A = A_0 \otimes \mathrm{Id}_Y$ acting on the Bochner space $L^p(\mathbb{R}^d , h^2_\kappa; Y)$, where $A_0$ is the Dunkl Laplacian, $h^2_\kappa$ a weight function invariant under the action of a reflection group and $Y$ is a UMD Banach lattice. We follow hereby a transference method developed by Bonami-Clerc and Dai-Xu, passing through a Marcinkiewicz multiplier theorem on the sphere. We hereby generalize works for $A_0 = − \Delta$ acting on $L^p(\mathbb{R}^d,dx)$ by Girardi-Weis, Hyt\"onen and others before. We apply our main result to maximal regularity for Cauchy problems involving $A$.