M.K.
I think that it is normal for 2year olds to want to carry things stuff/things around with them...keep their things close to them (but maybe not that close...LOL). I would ignore it as much as possible and make sure that she has pockets to put things in...or even a fannypack or apron to keep her "things" with her. Don't make a big deal about it, just remind her that pockets are where we keep things. Good luck!!