Can't you say "The girl has no animal"?
No, singular is "pigen har ikke et dyr"
Actually, more literally, the singular would be "Pigen har intet dyr".
Is "ingen" for plurals and "intet" for singular?
Ingen for -n and plural
Intet for -t
So Danish "ingen" must have the same function as German "kein-", am I right?