You might like to consider how the opening description of setting foreshadows the eventual death of both the scarlet ibis and of Doodle, who you are right to identify as being linked through symbolism in a very profound way. Consider the description that opens the story, and note the way that death is refered to:
The flower garden was stained with rotting brown magnolia petals, and ironweeds grew rank amid the purple phlox. The five o'clocks by the chimney still marked time, but the oriole nest in the elm was untenanted and rocked back and forth like an empty cradle. The last graveyard flowers were blooming, and their smell drifted across the cotton field and through every room of our house, speaking softly the names of our dead.
Note the way that this opening paragraph becomes strongly symbolic of the dead and the dying. Words such as "rotting" and "untenanted" and "rank" all bring to mind the death of various forms of nature, and let us not forget the way that in the opening sentence of the novel, the tree where the scarlet ibis settles is described as "bleeding." Lastly, the scent of the flowers in the graveyard provide an unescapable reminder of death and mortality.