Sleep well

It's otherwise possible, but actually having it stand up and be able to keep it's balance sounds like horseshit. (edit, it's not, they totally can) Also I don't think it intentionally bashed it's brains in to eat them, but I wouldn't be surprised they might when some spills. (And ai think OP would exaggerate, it'd probably be blood, but having some brain matter leak out isn't out of the question with it still being conscious, I think.

Like trying imaging a horse walking on two legs. It's just the anatomy doesn't really allow for it, even to the extent that cats and dogs do, which can do some steps.

Edit that was some utter bullshit guessing by me. Most wrong I've been about animals in a while, I think, got to own up to it.

Animals, and people, can and have continued to be alive and... somewhat, or even mostly functional... with portions of their brains obliterated or removed.

Go look up Phinneas Gage, or the history of lobotomies and brain surgeries.

Now, this person could be describing bloody chunks of the skull and skin and fur, but it is not strictly impossible that the deer could have actually managed to loose chunks of its actual brain, and still remain capable enough to keep functioning...

... for a while, at least. If it did really cave in its own skull, it would almost certainly die from cranial hemmoraghing soon afterward, if not that, infections.

Yeah that's really the part that makes me think it's exaggerated, misremembered, or just completely false.