A search is presented for same-sign top-quark production and down-type heavy quarks of charge -1/3 in events with two isolated leptons (electrons or muons) that have the same electric charge, at least two jets and large missing transverse momentum. The data are selected from pp collisions at sqrt(s)=7 TeV recorded by the ATLAS detector and correspond to an integrated luminosity of 1.04 inverse femtobarns. The observed data are consistent with expectations from Standard Model processes. Upper limits are set at 95% confidence level on the cross section of new sources of same-sign top-quark pair production of 1.4-2.0 pb depending on the assumed mediator mass. Upper limits are also set on the pair-production cross-section for new heavy down-type quarks; a lower limit of 450 GeV is set at 95% confidence level on the mass of heavy down-type quarks under the assumption that they decay 100% of the time to Wt.