Present study examines the pattern of variation of electric dipole moment (mu) and polarizability (a(p)) of impurity doped GaAs quantum dots (QDs) under combined presence of hydrostatic pressure and temperature and in presence of noise. Noise term carries a Gaussian white character and it has been introduced to the system via two different pathways; additive and multiplicative. Profiles of mu and a(p) have been monitored against the variations of hydrostatic pressure (HP), temperature and the noise strength. Under a given condition of HP and temperature, application of noise prominently influences the above two properties. However, the extent of influence depends on the noise strength and the pathway through which noise is introduced. The findings divulge feasible routes to control the dipole moment and polarizability of doped QD system through the interplay between HP, temperature and noise.