Though there are many things Scout does not understand, she is a very bright child.
The young Scout is a bright and curious child.
She can read and writer before entering school. Jem jokes that Scout was born with the ability to read. When Scout considers this idea, she realizes that she does not remember when she learned how to read.
The fact that she was able to pick up the skill of reading without direct guidance or instruction speaks to her innate intelligence.
She has taught herself to read, an indication of her intelligence, and is curious about many subjects.
Additionally, Scout has learned quite a few things about the law from Atticus and from watching him in the court room.
During the trial, the prosecuting attorney is described according to his usual tics and tricks. These are known to Scout, but not to Dill. This difference in knowledge helps to demonstrate some of Scouts additional or special attributes. She is not only smart, Scout also has some semblance of expertise.
On many occasions Scout also presents a skill for reading people and understanding subtle signs and signals. She appreciates Miss Maudie's habit of never laughing at childish slips of the tongue, understands Aunt Alexandra's gratitude to Maudie at the society party, and demonstrates a thorough knowledge of Jem's emotions as they are expressed physically.
when she starts school, she can already read and write
she gives her brother advice about a number of things