I'm not sure someone as selfish as Carol is willing to blow herself up with a nuke. Even if she was smart enough to ask them to teach her how to arm it.
Plus that in no way protects her from being infected. Once she is the nuke is useless.
Carol is on the clock for season 2. She's got a month or two at most. Plus she can no longer get anything from the hive with out risking conversion.
This is both the worst and best show. It's super slow but I still find it really interesting.