left-hander vs doer

left-hander and doer both are nouns.

Word	Noun	Adjective	Verb	Adverb
left-hander	Yes	No	No	No
doer	Yes	No	No	No

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

left-hander: a person who uses the left hand with greater skill than the right
doer: a person who acts and gets things done

Other hypernyms of left-hander include actor, worker.

left-hander (noun)	doer (noun)
a person who uses the left hand with greater skill than the right	a person who acts and gets things done
a baseball pitcher who throws the ball with the left hand