Should Dr. be included when citing a name like Dr. Seuss?

Yes. The MLA Handbook (sec. 1.1.2) provides the following guidance about titles in authors’ names: “If the name of the author of a source you consulted is given in the source with a title—such as Dr., Saint, or Sir—generally omit  the title in the works-cited list.” But this guidance does not apply to pseudonyms like Dr. Seuss, which may be treated as a unit and cited as follows:

Green Eggs and Ham, by Dr. Seuss, opens with the following famous first line: “I am Sam. Sam I am. Do you like green eggs and ham?” 

Work Cited

Dr. Seuss. Green Eggs and Ham. E-book, Random House, 1960.

Work Cited

MLA Handbook. 8th ed., Modern Language Association of America, 2016.