dancer vs doer

dancer and doer both are nouns.

Word	Noun	Adjective	Verb	Adverb
dancer	Yes	No	No	No
doer	Yes	No	No	No

As nouns, doer is a hypernym of dancer; that is, doer is a word with a broader meaning than dancer:

dancer: a person who participates in a social gathering arranged for dancing (as a ball)
doer: a person who acts and gets things done

Other hypernyms of dancer include actor, worker.

dancer (noun)	doer (noun)
a performer who dances professionally	a person who acts and gets things done
a person who participates in a social gathering arranged for dancing (as a ball)