To begin with, as you probably know, the New Critic would focus almost exclusively on this individual poem. New Criticism doesn't focus on the biography of the poet but does allow for discussions of allusions to earlier literary works and even to the place of this poem within a larger poetic tradition (such as the pastoral or love lyric). To avoid speaking about the poet, the New Critic would talk about the speaker (or "persona") in the poem. See the final paragraph of the essay "The Intentional Fallacy" (link provided below) for the discussion of allusiveness. Bruce Meyer's essay (see the second link provided below) provides a largely New Critical approach, focusing on the argument in the poem and on the imagery. You might also want to review Allen Tate's famous New Critical discussions of the poem (I couldn't find a link to these discussions, unfortunately, but maybe you'll have better luck).