I don't think you understand what advaita is. Everything that can be understood by the mind is unreal. Only the things beyond the mind is real. This is not only the teachings in the philosophy of advaita but also what Krishna says and means when he calls the world maya. It is also important to understand that although the importance of Vedas is high, the real can't be expressed in words, hence the Vedas may talk about what is real (like praising God and stating that he has innumerable qualities, he is infinite and so and so) but the texts itself cannot be real. Hence it must inferred that the eternity of the Vedas refer to the 'truthfulness' of the Vedas in context to (maya) world. I maybe wrong though (high probability).
Edit: For source, I will direct you to the first answer of According to ShankarAchArya in Advaita, is the universe "unreal" or "unworthy"?