Really? Even in big cities gossip goes around. If it’s not in your neighborhood, it’s at work, school, church, clubs, sports teams, etc.
In a town like that? People are talking and talking and talking. Maybe not being mean to her, maybe not looking at her weird, but they are talking. And these things are never forgotten. I live in a bigger town and some times people come to me and say stuff like “when he/she was young she did XYZ”. Nobody forgets the woman that killed her son, she has a normal life, people are civil with her, but everybody knows she did it and sometimes still comment about it.
If this girl stays in that town, and eventually has another child when she’s an adult, the future classmates of that future child will know and that poor kid will eventually find out too. Some things never change. And small towns never change either.