When Doodle is born, he is deformed and on the brink of dying. Everyone thinks he will die soon. The father even has a carpenter build a small coffin because they are so certain he will not survive. But Doodle does survive. The narrator wants a brother than can run, jump, and play outside. Mama cries and tells him that even if Doodle survives, he will never be able to do these things. The entire family looks upon Doodle as a very fragile child. When he is three months old, they are not even sure if he is "all there" mentally. So, their strategy is to keep him safe and sound, and out of the way. He's too vulnerable to be a part of their daily lives. That's why they put him in the front bedroom on a rubber sheet. Brother even supposes that Doodle might spend his entire life there. Doodle is different, and although his family (namely his mother) loves him, they do look upon him like he is an outcast.
But when Doodle grins at the narrator, he concludes that Doodle is "all there." When Doodle is two years old, he starts crawling. This is the moment when he first starts to act like a "normal" child in the eyes of the family. This is when they bring him out of the front bedroom.
But he learned to crawl (it was his third winter), and we brought him out of the front bedroom, putting him on the rug before the fireplace. For the first time he became one of us.
They symbolically bring him out of the outcast room and into the main social setting of the family. The fireplace symbolizes the heart of family life and this is the moment when Doodle is symbolically welcomed as "one of us."