While the book doesn't specifically say what Cindy Lou carries around with her, it mentions she has a "tiny little bed", which implies she might carry around a blanket or stuffed animal for comfort.
It's also fair to assume she carries a few toys, as children her age usually do.
Ultimately, what Cindy Lou carries around is left to the imagination, but it's likely she has some comforting items that remind her of home and make her feel secure.