A friend of a friend has a daughter named
Dolores who's around 5, so yup I can see it on a child, and I can see it getting some use in a small way. Afaik they don't use a nickname.
Lola is pretty popular as a stand-alone here, thanks to a kids' tv series (
Charlie and
Lola) and
Dolly has charted too.
I've never seen
Delores and it looks odd to me. Reminds me of DeLorean cars.