Propagation of light by Anderson localization has been demonstrated in micro-nano-structured fibers. In this work, we introduce a phase separated glass Anderson localization optical fiber for quantum applications. By using a spontaneous parametric down-conversion source, multi-photon detection with a single-photon avalanche diode array camera, and signal post-processing techniques, we demonstrate quantum light transport, where spatial correlations between photon pairs are preserved after propagation. In order to better understand and improve light transport, we study light localization, observing a dependence on wavelength. Our results indicate that the proposed phase separated fiber may become an effective platform for quantum imaging and communication.