This Letter presents what we believe is the first experimental study of frequency doubling of a Raman fiber laser (RFL) with random distributed feedback (RDFB) in an MgO:PPLN crystal. We compared two laser configurations, each with a half-open cavity. The cavity contained either a broadband Sagnac mirror or a narrowband fiber Bragg grating (FBG). We found that spectral broadening in the studied configurations of the RDFB RFLs differed from that found in a conventional RFL with a linear cavity, as well as from each other. We also compared the second harmonic generation (SHG) efficiency for these three types of lasers. The highest SHG efficiency was obtained for the RDFB RFL with the FBG delivering >100 mW power at 654 nm.