Where does the nap in kidnap come from and is napkin related Etymology Request

Two completely unrelated words that happen to collide in spelling, and your daughter has picked a genuinely good example.

Kidnap is late 1600s, and it's built from kid meaning child, which was already slang, plus nap meaning to snatch or seize. That nap is a variant of nab, the same one still alive in getting nabbed. The word appears in the context of children being seized and shipped to the American colonies as labour, and interestingly the agent noun kidnapper shows up first, with the verb kidnap looking like a back-formation from it.

Napkin is a couple of centuries older and comes into English from Old French nape, a tablecloth, ultimately Latin mappa. English then added the diminutive ending -kin, the one in lambkin and manikin. So napkin is literally a little tablecloth.

The nap on fabric, the fuzzy surface of velvet, is yet a third word from Middle Dutch. Three unrelated naps, one spelling.

The map inside mappa is the same one as in map, incidentally. A map was a cloth with a chart drawn on it before it was a piece of paper. Napkin and map are cousins and kidnap is a stranger to both.

Sleeping nap is a fourth one, from Old English hnappian, to doze. So the score is four independent naps, which is a decent haul for one syllable.

Worth telling her the general principle too: in English, two words looking alike is weak evidence and often no evidence at all. Ear on your head and ear of corn are unrelated. It's a fun thing for a curious eight year old to have in her pocket.