If at all possible, accompany children into public restrooms. When a child becomes too old to go into restrooms of the opposite sex, stand outside and wait for the child's return. Be observant of the time and of cries for help. Never consider a dog an added safety factor you can depend on. Dogs are not proven to be reliable deterrents to criminals.
Dogs are often unpredictable in times of stress.
Stores are full of strangers. Malls and stores are often chosen by people who do bad things because of misconceived perceptions of safety by other people who will then let their guard down. Let your children go only if they are in a reliable group or with an adult.