I have an answer of my question: It is $$\hat{A}\cong\widehat{ \bigoplus_{[\pi]\in Irr(A)}K(H_{\pi})}\cong \coprod_{[\pi]}\widehat{K(H_{\pi})} ,$$ everything is endowed with the ker-hull-topology. Now, the $K(H_{\pi})$ are simple, it follows $\widehat{K(H_{\pi})}=\{[id_\pi]\}$ and $\hat{A}$ is a disjoint union of onepoint-sets. It follows that the ker-hull-topology on $\hat{A}$ is the discrete topology.
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