I agree with the above post. The episode involving Mrs. Dubose is the last experience Scout and Jem will share as children. Everything after this (particularly the trial) will be observed, felt, and analyzed differently between the two. Scout maintains her innocence, and a major conflict in the later parts of the book will be her attempt to understand why Jem thinks/acts the way he does. Jem, on the other hand, has little time for Scout, and he processes each new development in the trial quite personally.
By ending the first part with the Mrs. Dubose episode, Lee is also introducing an important lesson to the children. Think of it as a last attempt to fortify their defenses before they are forced into situations beyond their years. Prior to this, Atticus often tells Scout to keep her head when times get rough, and Mrs. Dubose seems to be the testing ground before they face the rest of the community. Thus, they have one final instruction in courage and grace before they have to actually practice those values.
In my opinion, part one of the book focuses on the childish world of the Scout, Jem, and Dill. Their main focus and concern is with playing children’s games such as the make believe plays about the Radley’s.
The second part of the book focuses more on their exposure to an adult world as the novel shifts its focus from the Radleys to the Tom Robinson trial. The children are exposed to real world problems and lose interest in the childlike world of make believe. We later see they are not immune from the dangers of the adult world as they are thrown into a world of hatred and racism. .
Harper Lee chooses to end part one after chapters 10 and 11 because as mentioned, they are the last of the children's childhood experiences. Once the trial of Tom Robinson begins, Scout and Jem will be exposed to the cruel, adult world.