Pudding by Pippa Goodhart
Nobody wants Pudding, the tubby pup and nobody wants Lucy, the lonely little girl. They are very sad - and then Pudding is bad, and chews up everything in sight. Both of them decide to run away into the woods - where they meet each other by chance. Lucy likes Pudding and Pudding licks Lucy, and so they play together, and stay together, forever. Very simple and very sweet.