Although kids this age can pick up most things just fine, they don't yet have the strength or coordination that carrying stuff around requires. So when she needs to bring something like a pillow or a big stuffed animal from one room to another, she'll probably pull it along behind her. There are benefits to this mode of transport: Your wobbly novice walker can use a sturdy item, such as an oversize teddy bear, to steady herself.
By age 2, she'll be stronger and more adept at manipulating objects, so trailing them behind her will be a thing of the past. Time to start sweeping again.