(not a teacher)
I've never heard of "a check of."
"A check on the baby revealed that it was still sleeping." sounds correct.
"A check of the baby revealed..." is ambiguous because, as odd as it sounds, it might mean that the baby did a check. Given the context, it should be obvious that the baby is sleeping, but still it sounds odd.
Also, when used as a verb, you hear "check on." For example: "Check on the soup to make sure it is not boiling over." In this sentence, you are commanding someone to inspect soup.