She was upset about killing, doesn't mean she wasn't going to be prepared to kill to survive. If anything, Carol isn't stupid. As she said in the note, the reason she left was to leave behind the influences that would make her kill more and more, aka protecting her new family.
So the solution is to sew a damn uzi inside of your sleeve and increase your chances of killing by 100% driving on a main road with plenty of open space in a car that looks like it was designed for Fury Road? She knows Negan's army is crawling all over the place looking for who murdered a bunch of their people and chooses THIS as her path to avoid killing..?
Not following the logic here. She's a smart character who is being written into the ground with ridiculous and moronic decision making.