They were generally present beginning in the 1980s. The phone you linked is from the 1960s. The layout with Q and Z was standardized by ITU-T in 1988 https://en.wikipedia.org/wiki/E.161
Earlier in time the letter "O" was also not generally on phone keypads.
According to your link, Q and Z were officially added sometime in the 1990’s, in a later revision. That puts the official change well into my childhood, which explains my out-of-date information; I didn’t put much effort into researching my comment.
Earlier in time the letter "O" was also not generally on phone keypads.