  For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function
$k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Let $L=-\Delta +V$,
$V\geq 0$, be the Dunkl--Schr\"odinger operator on $\mathbb R^N$. Assume that
there exists $q >\max(1,\frac{\mathbf{N}}{2})$ such that $V$ belongs to the
reverse H\"older class $\text{RH}^q(dw)$. We prove the Fefferman--Phong
inequality for $L$. As an application, we conclude that the Hardy space
$H^1_{L}$, which is originally defined by means of the maximal function
associated with the semigroup $e^{tL}$, admits an atomic decomposition with
local atoms in the sense of Goldberg, where their localization are adapted to
$V$.
