We show that quantum frequency conversion (QFC) can overcome the spectral distinguishability common to inhomogeneously broadened solid-state quantum emitters. QFC is implemented by combining single photons from an InAs/GaAs quantum dot (QD) at 980 nm with a 1550 nm pump laser in a periodically poled lithium niobate (PPLN) waveguide to generate photons at 600 nm with a signal-to-background ratio exceeding 100:1. Photon correlation and two-photon interference measurements confirm that both the single photon character and wave packet interference of individual QD states are preserved during frequency conversion. Finally, we convert two spectrally separate QD transitions to the same wavelength in a single PPLN waveguide and show that the resulting field exhibits nonclassical two-photon interference.