I'd venture to say that it 's the song that IS "Daddy Dear"...because it appears that Brian was remembering a song called "Little Child," released as a single by Eddie Albert and Sondra Lee in 1956:
https://www.youtube.com/watch?v=inIv0gOhhnEThe tape that we have of Brian playing the song would appear to be an instance of him trying to remember what he probably heard when he was 14, as "Little Child" was a reasonably-sized hit at the time, and it certainly has the type of sonic and emotional content that would have registered in the Wilson household.
So rather than "Daddy Dear" being a never-finished Brian song, it's really another of the (potential) cover versions that have bubbled up over the years, a la "Ol' Man River," "Gimme Some Lovin'," and "Proud Mary." [It appears that this fact has been well-established for some time, as it is mentioned in a thread about the "Daddy Dear" tape from the Hoffman board way back in 2006.]
There's also an instrumental version of "Little Child" by Wes Montgomery that was released on his 1966 LP TEQUILA:
https://www.youtube.com/watch?v=kVvqGL3EAXYA version that has more of the floridly emotion approach of the rendition in THE NAKED KISS is the one by Cab Calloway and his daughter, also from 1956:
https://www.youtube.com/watch?v=b85EPad0yPw[With its reference to "the bluebird of happiness," this song] certainly fills out the trifecta of "bird" songs, following on the heels of Dennis' "Little Bird" and Al's "At My Window"...