A search is presented for heavy-quark pair production (Q (Q) over bar) under the decay hypothesis Q (Q) over bar -> W(+)qW(-)(q) over bar with q = d, s, b for up-type Q or q = u, c for down-type Q. The search is performed with 1.04 fb(-1) of integrated luminosity from pp collisions at root s = 7 TeV collected by the ATLAS detector at the CERN LHC. Dilepton final states are selected, requiring large missing transverse momentum and at least two jets. Mass reconstruction of heavy-quark candidates is performed by assuming that the W boson decay products are nearly collinear. The data are in agreement with standard model expectations; a heavy quark with mass less than 350 GeV is excluded at 95% confidence level.