Factual error: Season 5 and they are still driving cars around! Gasoline won't last years unless specially treated.
Other mistake: Most if not every time someone kills a walker in close proximity or repeatedly bludgeons one that is already dead with a blunt object and there is a CGI blood spatter effect (as opposed to a practical blood spatter effect), the blood magically never gets on the person's face.
Answer: No, she actually tries to talk Rick out of it, but he's already made up his mind, minutes later when Daryl asks him about the location of his brother Lori says "he'll show you."