Correct grammar would be: Why do you have money, but I don't (do not)?
Use 'do' when the subject is I, you, we or they. Use 'does' when the subject is he, she or it. In this case, the subject is you in the first phrase and I in the second.
Why does he have money, but I don't? In this example, does is used since the subject is he in the first phrase.