One defintion of Quaternary
Of or belonging to the geologic time, system of rocks, or sedimentary deposits of the second period of the Cenozoic Era, from the end of the Tertiary Period through the present, characterized by the appearance and development of humans and including the Pleistocene and Holocene epochs.
I think it depends on what units of geological time you are using: eons, eras, periods or epochs. There is shown on a geological timeline at
http://www.yourdictionary.com/images/ahd/jpg/A4geolog.jp g
So I think QUATERNARY period or PLEISTOCENE epoch are both correct. It all depends on your unit of time.