That example can't exist with natural darkness in the real world because natural darkness doesn't exist as a volume-filling concept (instead darkness is the lack of perception of light on a particular vector). It can kind-of-sort-of exist in the abstraction of D&D if you approach the rules as defining the physics of the game world, but unless I'm mistaken I don't think you approach the rules as an alternative physics engine.If this was regular darkness and the bunny was there, what would the dog see? IMO. It will be the same.
If one did use the very vague obscurement rules to try to define the physics of light in the D&D world, it would still be up to the DM to determine what could be seen in the example, as the rules aren't complete enough to create a well-defined system.