I liked the entire episode, including the disarmament. I think this series gets people to thinking about things in a way they never would otherwise. The question of who carries certain weapons (if they get one at all) is something that will surface then. Hell, it exists now, only it is state and federally run. Personally, I think it was irresponsible for her father to give her a pistol and teach her nothing about how to use it. However, I would have given her an intensive, educational lecture about what things to consider when you operate a firearm, emphasizing not to use it except at very close range since she probably couldn't hit the target, would waste ammo and shoot something she shouldn't.
Just because she wasn't trained doesn't mean she is a dumbass. She still has the right to defend herself with effective weapons. If a person is logical enough to understand when to shoot and when not to shoot, as well as how to safely handle and maintain a firearm, that person has a right to carry it. If you trust a woman like that enough to watch your two kids, not to run off with supplies, and not to freak out like a madwoman, you can probably trust her not to be a total dipshit and shoot someone. Most of us were probably exposed to firearms as children, learning firearm safety and common sense. Adults are much more capable of processing this information and using sense in operating a firearm. Sure she would need training to be able to be proficient in its use, but who are any of you, or me, to decide she does or does not get one if the one time she fires it is to save her life at point-blank range? As long as she knows she cannot be Rambo and should act very conservatively, I don't see it as being a huge problem, in Walking Dead or other similar scenarios where constant threats exist.
For those who skimmed my paragraphs, I'll list my qualifier again: If you trust a person enough to not worry about your family, your friends or your supplies around them, you can probably trust them to listen to what you have to say when instructing them in the use of a firearm. If you give them the basics of safety and teach them to be very conservative in its use, I don't see a problem arising. There are some people who have common sense and who are just uncomfortable with firearms, and that's okay, but just because someone doesn't have intensive training doesn't mean someone can deny them their right to self-defense.
In My Opinion.
Your Mileage May Vary.
And all the rest....