When Doodle goes out to see the ibis in the bleeding tree, Brother notices that Doodle's "hands were clasped at his throat" and that he had never seen Doodle stand so still for so long. Doodle appears worried. He notices how unsteady and vulnerable the ibis looks and maybe he thinks of his own vulnerability, so he protects his own neck.
After the ibis dies, Doodle is too affected to eat. He kneels down beside the bird but his mother warns him not to touch it. His father buries the bird and the family goes inside to eat. Doodle still has no appetite and Brother notices how pale Doodle looks. Doodle feels sorry for the bird. He also sympathizes and empathizes with it. Sympathy is when you feel sorry for someone. Empathy is when you feel a person's pain as if it is your own. Doodle empathizes with the ibis because he is also vulnerable. He understands what the bird felt as it was perched precariously in the tree and as it fell to the ground.
Recall that his father had a coffin made when he was born because no one thought he would survive. They kept the coffin and with that and Doodle's disabilities, he is always reminded of his vulnerability and potential to die young. The ibis's death is a sad event but it also reminds Doodle of his own vulnerability and mortality and it scares him.