I know little of this (intriguing) subject so this is more a series of questions than an answer.
First, what is the role of the 'image' in imagination? I think it must be central. (Though maybe not essential; concepts like 'I'm hungry' don't seem to require it, though you could argue that's just thinking not imagining - although 'will I be hungry this afternoon if I don't eat now?' is potentially more like imagination and still doesn't seem to require an image).
Anyway, if the image is central then functional MRI of an animal's visual cortex while the animal is 'imagining' something could be revealing. My proposed way of doing that would be during a dream, as I'd define a dream to be an unconscious imagination or conversely an imagination to be a conscious, directed dream.
I expect all sentient animals do, or at least might, dream: dogs really do look like they're chasing cats, or running through some experience, in their sleep.
So could you examine a dog in sleep with fMRI? It seems feasible, as long as the dog is comfortable with it.