Dreams featuring animals often carry significant meanings related to our instincts, emotions, and relationships. In your dream, the cat in the hat could symbolize playfulness or creativity, perhaps reflecting a whimsical or unconventional aspect of your personality. The act of the cat eating a rat could represent overcoming fears or negative thoughts, as rats are often associated with unpleasantness or treachery.

The cat then sitting on your dog's back might suggest a dynamic between different aspects of your life or relationships. Dogs often symbolize loyalty and friendship, so this could indicate a playful or unexpected shift in a relationship where creativity or fun is taking precedence over loyalty or seriousness.

Overall, this dream may be encouraging you to embrace a more playful side of yourself and explore new ways to navigate your relationships. Consider what areas of your life might benefit from a lighter, more imaginative approach.