What is the name of this book series?

I am looking for a series of books about 6-7 kids who live in a post-apocalyptic world and live together. All the adults have been killed off by a disease and most of the kids (aside from the main characters) died from lack of survival skills. The characters are Teacher, the oldest who teaches the youngers ones; Hunter, who steals food from (now-abandoned) grocery stores; and Mother, who acts like...well, a mother. The little kids are named Teddy Bear, Action Figure, and Dolly. One day a guy shows up carrying a mannequin (named Bad Guy) in a backpack. He tells them that they should go find the President because he can solve everything. There is also a couple of toddlers named Puppy (who thinks he's a puppy) and Kitty (who thinks she's a kitty.) Also, Bad Guy loses his legs sometime in the first book. I know all of this happens but I can't remember what the title of the book is, and I can't find it by searching the main characters names (I've tried, though.) Thank you to whoever helps.