"This Land" does NOT use "Little Darling Pal of Mine" for its tune, but another Carter Family-recorded song, "When the World's On Fire" (I think that's what it's called).
"Little Darling Pal" only resembles either of the other songs in the first four notes, which are do, re, mi, fa, so are hardly distinctive. You could cite the bass runs to play "Study War No More" and get closer to "This Land" than "Little Darling."
But citing similarities between tunes isn't really about composer credits anyway, is it?