That's where the show gets a bit unrealistic. A woman would always value life much more than a man and be less apt to kill.
In my opinion, the show is more realistic that your perceptions. In the everyday nonconflicted world, women (in general) would lend towards a tend-and-befriend philosophy, seeking less violent resolutions ensuring protection for children, mates and accepted associates. In the fictional world of
The Walking Dead, people's actions are dedicated to survival every single waking moment. Resources are extremely limited and personal/group security is threatened constantly.
She would indiscriminately kill anyone including those of her group if she was a serial killer ( @
BrAinPaiNt ). Carol values the lives of everyone in her social dynamic group because they are essential to resource gathering and security while maintaining an emotional constant for her. She would kill anyone threatening her environment. I believe her character would be more typical of women existing in such a world than atypical. Genetics may encourage more or less personal empathy but not stupidity necessarily.