This work examines the role of spatial impurity extension (SIE) on a few nonlinear optical (NLO) properties of impurity-doped GaAs quantum dot (QD). The NLO properties considered are the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG). The study also includes 1 (GWN) which has been incorporated into the doped QD through additive and multiplicative pathways. The study uncovers the delicate interplay between GWN and SIE which ultimately fabricates the said NLO properties. NOR, SHG and THG manifest red-shift with enhancement of SIE both with and without GWN. The study also shows possibilities of attaining maximum NLO response by prudently applying GWN in a particular pathway. Depending upon the particular NLO property concerned, the presence of noise and its mode of application can either deplete or amplify it to different extents with respect to the noise-free situation.