“Oh Daddy” is a classic blues recorded for the Black Swan label in 1921 by Ethel Waters. The original orchestral arrangement has a Broadway feel, and the song is written in a typical Tin Pan Alley form, with a verse that sets up the story, but never repeats, and a chorus that is really the main body of the song.
A couple of techniques I use to fatten up the sound of the solo guitar are thumb rolls and melody matching with voice and guitar. Thumb rolls are easiest to play with a bare thumb and consist of letting your thumb roll off the string you’re picking to hit one or two additional strings on the way down. It should feel more like a little strum than picking an individual note.