There was a time after Alderaan where Leia would have fired without a second thought, no matter how cute and innocent five-year-old Darth Vader looked, but things were different after Endor. She was willing to give her life for the Rebellion, but not to erase her brother or the possibility that this boy might grow up better. Good thing for the galaxy, she had no such compunctions about killing Palpatine.
Grandfather Paradox