You see... although vertex covers and dominating sets are different concepts, a vertex cover which is also an independent set is equivalent to a dominating set which is also an independent set, i.e. an independent dominating set.
(Independent) dominating sets are hard in general graphs. The paper above discusses a linear-time approximation for unit disk graphs. Hope it helps.
For bipartite graphs, a vertex cover is also an independent set. Since sum covering number and independence number of a graph is the number of its vertices, I think only bipartite graphs can have their vertex cover is an independent set.