dotage vs old age

dotage and old age both are nouns.

Word	Noun	Adjective	Verb	Adverb
dotage	Yes	No	No	No
old age	Yes	No	No	No

As nouns, old age is a hypernym of dotage; that is, old age is a word with a broader meaning than dotage:

dotage: mental infirmity as a consequence of old age; sometimes shown by foolish infatuations
old age: a late time of life

Other hypernyms of dotage include age, eld, geezerhood, years.

dotage (noun)	old age (noun)
mental infirmity as a consequence of old age; sometimes shown by foolish infatuations	a late time of life