In section 26 of "Song of Myself", Whitman wrote:
I hear the train’d soprano (what work with hers is this?)
The orchestra whirls me wider than Uranus flies,
Who knows the meaning of the sentence in parenthesis? (what work with hers is this?)
'What work with hers is this?' would perhaps be better read as: What work, with hers, is this?
I believe he is referring to the song being performed. The phrase suggests a feeling of wondering from the narrator. He asks (metaphorically) what work (piece of music) with her own work (singing) as accompaniment, is being played.
A more natural version for modern ears might be something as simple as 'What is this song?!'