Mood and tone in poetry are closely connected and sometimes cause confusion because they both deal with the emotions centered around the poem.
The tone of a poem relates to the intentions of the poet/voice in the poem. Desiderata was written by Ehrmann specifically for his daughter and the tone is clearly didactic - intended to provide good objective advice - but is gentle rather than firm.
The mood of a poem relates to the atmosphere of a poem, and to some extent, the feelings that it arouses in a reader. Some of the adjectives that I might choose to describe the mood of Desiderata are - calm, contemplative, peaceful, thoughtful, enlightened. A different reader might interpret it differently -perhaps dependent upon the extent to which s/he is willing to accept advice.