baby's room vs child's room

baby's room and child's room both are nouns.

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

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

baby's room (noun)	child's room (noun)
a child's room for a baby	a bedroom for a child