How is 古代汉语 defined?
古代汉语 is everything that is not 现代汉语. More precisely, we have 上古汉语 (Old Chinese: Oracle bones, Warring states, Qin; Classical Chinese: Spring and autumn, Han）, 中古汉语 (Middle Chinese: Tang, Song) and 近代汉语 (mostly late Qing).

博士 was coined in the Warring states period, according to zdic.net. Disyllabic words have always existed, although the ideal used to be monosyllabic word characters.