Just seen this. Best of luck.
My youngest took the end of his pinky off in a door about 6 months ago. It sounds very similar to your wee one’s injury, he was about 3 at the time and cut off at the base of the nail.
The medical folks were brilliant and we had a plastic surgeon reattach it that evening. Now, you wouldn’t know it had ever been injured. Well, if you look really closely you can just about make out a scar. They seem really not bothered at that age (amazing) and their powers of healing are impressive. He was in a boxing glove bandage for about 3 weeks (from memory, might have been 4). It took a month or two of the nail to fall off and grow back again.
Anyway – hope it all goes well! Hopefully, he’ll not even have any real scar to show off!