Through first-principles molecular dynamics we study the low-temperature oxidation of the Si(001) surface from the initial adsorption of an O-2 molecule to the formation of a native oxide layer. Peculiar features of the oxidation process are the early, spontaneous formation of Si4+ species, and the enhanced reactivity of the surface while the reactions proceed, until saturation is reached at a coverage of 1.5 ML. The channels for barrierless oxidation are found to be widened in the presence of both boron and phosphorous impurities.