Answer:
Step-by-step explanation:
Yes, Rikki-tikki-tavi was willing to die to protect Teddy. In the story "Rikki-tikki-tavi" by Rudyard Kipling, Rikki-tikki fights and kills the two cobras, Nag and Nagaina, to protect Teddy and his family. During the final fight with Nagaina, Rikki-tikki risks his own life to grab hold of her and prevent her from escaping into her hole, saying, "She will kill and kill and kill and never be satiated. I have known her eggs for years and years. She lay eggs underground, and they are as hard as iron. She has thirty great overgrown eggs in a rat hole now. I must get her out of the way, and when I have killed her you must take out the children and search for the eggs. They will behid in some crevice, and you must have them hatched, and then you must feed and feed and feed, till they are strong enough to burst out." In doing so, Rikki-tikki puts himself in grave danger, but ultimately succeeds in defeating Nagaina and protecting Teddy and his family.
Cite: "Rikki-Tikki-Tavi" by Rudyard Kipling that supports the idea that Rikki-tikki-tavi was willing to die to protect Teddy:
"Rikki-tikki felt his eyes growing red and hot (when fighting Nagaina); he stood up and fluffed out his fur to get the rain off of him, and then he bowed very low and said, 'It was I that killed Nag, but I did not kill Nagaina. She will go the way of the rest of the vermin in this house, and if you don't go with her, it's your own fault.' With a scream and a bound, he was on her, burying his teeth in the folds of her neck, hind legs making a racket as he struck and tore." (Chapter 8)
This quote shows that Rikki-tikki-tavi was willing to fight Nagaina, the deadly cobra, to protect Teddy and his family, even though he knew it could be a deadly battle.