child's room vs bedchamber

child's room and bedchamber both are nouns.

Word	Noun	Adjective	Verb	Adverb
child's room	Yes	No	No	No
bedchamber	Yes	No	No	No

As nouns, bedchamber is a hypernym of child's room; that is, bedchamber is a word with a broader meaning than child's room:

Other hypernyms of child's room include bedroom, chamber, sleeping accommodation, sleeping room.

child's room (noun)	bedchamber (noun)
a bedroom for a child	a room used primarily for sleeping