A Brillouin random fiber laser (BRFL) based on a low-concentration erbium-doped fiber is proposed as an active distributed feedback medium. Using a 980 nm pump source, a custom-made 25 m erbium-doped fiber with an ion mass fraction of 0.0035% serves as the Rayleigh scattering medium, providing distributed random feedback to achieve laser resonance. Compared to a traditional 20 km single-mode fiber (SMF), the erbium-doped fiber significantly enhances the distributed Rayleigh scattering intensity by approximately two orders of magnitude. This compact BRFL, leveraging the low-concentration erbium-doped fiber, demonstrates excellent laser noise suppression and frequency stability. Experimental results indicate that the proposed BRFL reduces relative intensity noise by about 20 dB and decreases frequency jitter over time by 64.3% compared to a BRFL using 20 km of SMF as the feedback medium. The active amplification of Rayleigh scattering in the erbium-doped fiber introduces optically controllable disorder, enabling the BRFL photonic system to display manipulated statistical properties of the dynamic spin glass phase. Moreover, the experimental observation of optically controlled replica symmetry breaking offers new avenues for exploring laser physics and nonlinear phenomena.