"Je n'ai pas de chien mais deux" isn't entirely correct (as I understand it). What you are saying is "I don't have A dog but two." You really want to say "I don't have ONE dog but two." Therefore you'd say something like: "Je n'ai pas un chien mais deux." This is better -- and grammatically correct -- but a native speaker wouldn't say it this way either, I believe. You would hear something like: "Je n'ai pas juste un chien, j'en ai deux." Which translates to "I don't have just one dog, I have two of them."

-- Chris (not a native speaker)