age vs dotage

age and dotage both are nouns.

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

As nouns, dotage is a hyponym of age; that is, dotage is a word with a more specific, narrower meaning than age:

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

Other hyponyms of age include second childhood, senility, autumn years, decrepitude.

age (noun)	dotage (noun)
how long something has existed	mental infirmity as a consequence of old age; sometimes shown by foolish infatuations
a time of life (usually defined in years) at which some particular qualification or power arises
a late time of life
an era of history having some distinctive feature
a prolonged period of time