1. It's an anchor.
Just as everyone has already said, she wants a reason to see you again once she gets back (and possibly a stimulus to spark memories of her while she's gone). Cool, BUT this is low self-esteem behavior and another way of saying she doesn't trust you enough yet not to forget her. You should be able to reassure her, if the situation should arise, that this is unnecessary.
Honestly it's a bit of a stab at you as a man implying weak integrity. I doubt she would even realize that, but that's what it is.
2. It's a sh*t test.
I don't know why nobody has mentioned this yet, but this is just as likely. Reasonably you don't know her well enough yet for her to ask this of you. Allowing this could imply that you are either a) a "nice guy" or b) a pushover, neither of which help in building or maintaining attraction.
In either scenario I would still suggest not taking her stuff, though not shutting her down outright. Say you don't have room or something along those lines.
To parallel this to my own life, I've known my current girlfriend now for three years and have been dating exclusively for nine months. A few months ago she asked to leave a toothbrush at my place. I said no, to keep a travel one in her purse. Last week I mentioned moving and she shared that we could live together because it would make rent cheaper; I said no. Some would say that I'm being a rigid, unnecessary prick; I would say she's infringing upon my independence and you can't put a price on that.
Just my thoughts.