The doctor plays a behind the scenes role. He isn't described, or named. He isn't in any actual scenes. Still, he plays a big role in driving the events of this story, and he contributes heavily to the tragedy. He seems to be behind the fact that "everybody thought [Doodle] was going to die," and Mama's fear that Doodle "might not […] even be 'all there'" (1.3, 1.4). He's tells the family that "the strain" of learning to crawl "would probably kill" Doodle because of his "weak heart" (2.1). He also tells the family that Doodle is incapable of ever walking.
First of all, heart disease, especially congenital heart disease (i.e., born with heart disease), was very mysterious in those days. Doodle lived between 1911and 1918. The stethoscope wasn't even invented until 1916, just two years before Doodle's death. The doctor probably listened to Doodle's heart by putting his ear directly to Doodle's chest. For many years the primary treatment received by people with heart problems was exactly what the doctor prescribes for Doodle – rest. Furthermore, a child born with physical disabilities was often assumed to have deficiencies in brain function as well. The doctor was probably doing what most doctor's would have done – encouraging the family to treat Doodle delicately so as not to overwork his fragile heart, and warning them not to expect him to live, much less lead a high-functioning life.
Doctor's today know that exercise is important for everyone, including heart patients. Of course, not all heart patients are the same. Some babies born with heart conditions are indeed too fragile to do half of what Doodle did. Luckily, there are also surgeries and medications available for many of those babies. We don't mean to suggest that today's heart science is perfect. There are still fatalities, misdiagnoses, and all sorts of complications.
So, on the one hand, the doctor was just doing his job, practicing medicine according to the standards of his time. On the other hand, Brother, a child, seems to intuitively understand that Doodle is much stronger than the doctor says, and capable of much more than the doctor says he is. Our main point is to show that Brother is not the only one guilty in Doodle's death. If he'd had a little help from a perceptive doctor, willing to compromise, he might have been able to understand that Doodle was fragile, and did need special care, but that he could still lead an active physical life.