Dinah was the fictional pet cat kept by Alice, the main character of the children's book Alice's Adventures in Wonderland.
Early on in the story, Alice had began to dream: she and Dinah were hand-in-hand, and Alice earnestly asked Dinah if she had ever eaten a bat. (DIS: "Light and Shadows")
The book did not make a physical appearance, but rather a visual of the pages was seen as Amanda Grayson recalled reading the story to Spock as a child. Only left parts of the page were seen, but enough to reconstruct the narrative. The full sequence reads as follows: "She felt that she was dozing off, and had just begun to dream that she was walking hand in hand with Dinah, and was saying to her very earnestly, "Now, Dinah, tell me the truth: did you ever eat a bat?" when suddenly, thump! thump! down she came upon a heap of sticks and dry leaves, and the fall was over." The section is from chapter 1 of the book and can be read here.