Both Doodle and the Ibis are out of place. Doodle's family recognizes his vulnerability and therefore they treat him as if he could die at any moment. They care for him but regard him as somewhat of an outcast. This only begins to change when he starts to exhibit more "normal" behavior. They keep him segregated in the front bedroom. When he learns to walk, they bring him into the living room and this is when he finally "became one of us." Likewise, the ibis is an outcast. Father supposes that a storm blew the ibis off course from the south. It is in an environment it is not used to and doesn't know how to appropriately adapt.
The main similarity between Doodle and the ibis is vulnerability. Damaged from the storm, the bird's wings don't work properly. It should be able to fly down from the tree but it tumbles awkwardly and falls to its death. Doodle is also saddled with a body that doesn't work as well as Brother's does. He tries to run and do all the things Brother can do, but his frail and vulnerable body can not keep up.
Doodle recognizes how he and the ibis are both vulnerable and out of place. He sees the bird struggle to survive only to awkwardly fail. Doodle struggles to live up to Brother's concept of a "normal" brother. Doodle is so affected by the ibis's death that he won't eat dinner and he insists on burying the ibis himself. When he comes in from burying the ibis, he is "pale," the color and (symbolically) the life drained from his face. Perhaps the ibis's death reminds him of his own little coffin and his own mortality.