The random Raman fiber laser (RRFL) has attracted great attention due to its wide applications in optical telecommunication, sensing, and imaging. The quantum defect (QD), as the main source of thermal load in fiber lasers, could threaten the stability and reliability of the RRFL. Conventional RRFLs generally adopt silica fiber to provide Raman gain, and the QD exceeds 4%. In this letter, we propose and demonstrate a phosphosilicate-fiber-based low-QD RRFL. There is a strong boson peak located at the frequency shift of 3.65 THz in the phosphosilicate fiber we employed. By utilizing this boson peak to provide Raman gain, we demonstrated an 11.71 W temporally stable random Raman laser at 1080 nm under a pump wavelength of 1066 nm. The corresponding QD is 1.3%, less than one third of the QD of the common silica-fiber-based RRFL. Compared with the full-cavity low-QD Raman fiber laser, this cavity-less low-QD RRFL has lower and flatter noise in the high frequency area (>100 kHz). This work provides a reference for suppressing thermal-induced effects, such as thermal-induced mode instability, thermal noise, and even fiber fusing in RRFLs.