I agree with the other expert. There really are NO diseases that could be transmitted by a rat bite to cause those signs and ensuing death. Rabies or leptospirosis are the only two diseases your dog could get from a rat, and neither of these would cause death so rapidly. Neither would cause bloody diarrhea and vomiting.
The rat bite was coincidental with her death. I strongly recommend having a necropsy performed to diagnose the cause of her death, and get closure.
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