Poor thing. Have you applied anything to the wound?
I had a quail who got scalped. You could see her skull. She coudn’t hold her head up and I didn’t think she would survive the night. I would have culled her right then but my strong shears/scissors hadn’t come yet, and I didn’t want to mess it up. If that had happened now I would have tried cervical dislocation, but too late now.
Came back the next day and she was running around. I then just put antibiotic ointment on it daily and she healed up just fine.
Of course hers wasn’t a bite. I’d be even more concerned about a rat’s mouth bacteria in this case.