Tone is the feeling displayed by the author toward the subject of the poem.
Mood is the feeling created by the poet for the reader.
It is a warm poem that talks about love and warm that you can obtain from having a puppy. It seems the author had a great love for his dog and wants to communicate and share that feeling to readers by inviting them to have a dog.
Well from what I remember from the poem Vern by Gwendolyn Brooks, it was about having a puppy as such a good companion, so in my opinion the tone seems to be warm and happy and I'm assuming the mood would be the same as well.
