There are actually several threads about the song LITTLE DARLING PAL OF MINE, plus a version in the DT. To see them, I suggest you start here and then follow the links at the top of the page to find the others.

But I'm puzzled by this request. LITTLE DARLING PAL OF MINE doesn't even contain the phrase "my little girl." By "Carter and Carter" I assume our guest means Sara & Maybelle Carter. A couple of albums exist of them alone; however, I don't see any title that resembles "my little girl."

There are lots of songs called MY LITTLE GIRL but I'm not finding any that were written or recorded by anyone named Carter.