Do you think that the narrator is to blame for Doodle's death in "The Scarlet Ibis?"

It is hard to blame the narrator ("Brother") completely because he is just a kid himself. He openly admits his responsibility in tormenting Doodle and pushing him too far, though, so the narrator is largely to blame.
Brother says Doodle was "a disappointment" from the beginning. Brother wanted a more physically able companion. As a result, he resents Doodle. Brother torments Doodle by showing him the casket that was meant for him.
Brother teaching Doodle to walk seems like a generous gesture to his parents, but Brother reveals he only taught Doodle to walk out of shame.

They did not know that I did it for myself, that pride, whose slave I was, spoke to me louder than all their voices, and that Doodle walked only because I was ashamed of having a crippled brother.

At the end of the story, when Doodle has "failed," Brother leaves him, literally and symbolically. Brother runs away faster and faster, knowing Doodle will push himself but inevitably be unable to keep up. As Brother runs away, he feels a "streak of cruelty." He runs faster and pushes Doodle to run himself ragged. He puts Doodle through physical and emotional strain and this becomes too much for Doodle's body to handle.