Loss and noise quickly destroy quantum entanglement. Nevertheless, recent work has shown that a quadrature-entangled light source can reap a substantial performance advantage over all classical-state sources of the same average transmitter power in scenarios whose loss and noise makes them entanglement breaking [1, 2, 3, 4, 5, 6], standoff target-detection being an example. In this paper, we make a first step in extending this quantum illumination paradigm to the optical imaging domain, viz., to obtain better spatial resolution for standoff optical sensing. Our canonical imaging scenario - restricted, for simplicity, to one transverse dimension - is taken to be that of resolving one versus two closely-spaced in-phase specular point targets. We show that an entangled-state transmitter, which uses continuous-wave-pumped spontaneous parametric downconversion (SPDC), achieves an error-probability exponent that exceeds that of all classical-state transmitters of the same average power. Using these error-exponent results, we find the ultimate spatial-resolution limits for coherent-state and SPDC imaging systems that use their respective quantum-optimal receivers, thus quantifying the latter's spatial-resolution advantage over the former. We also propose a structured optical receiver that is ideally capable of harnessing 3 dB (of the full 6 dB) gain in the error-probability exponent achievable by the SPDC transmitter and its quantum-optimal receiver.