This paper presents an experimental investigation of the spectral and power stability of a random fiber laser (RFL) based on nanoparticle (NP)-doped fiber, under three different passive optical feedback configurations: retroreflector, Faraday rotator, and fiber Bragg grating (FBG). The NP-doped fiber offers enhanced Rayleigh scattering and intrinsic gain, allowing distributed feedback and laser generation. Spectral analysis revealed that the FBG configuration presented the highest spectral stability, with a 91.25% reduction in wavelength variation compared to the retroreflector. The Faraday rotator also contributed to the spectral stability, with a 37.5% reduction. Regarding power stability, the Faraday rotator presented the best performance, with only 1.62% variation, while the FBG provided the highest output power (8.13 dBm), with a 6.1% variation. The retroreflector configuration demonstrated the worst performance in both spectral and power stability. These results confirm that the combination of NP-doped fibers and well-selected passive feedback elements allows the development of more stable and coherent RFLs, expanding their potential for application in sensing, telecommunications, and optical fiber devices.