Symbolism, Imagery, Allegory
Monica's doll makes very few appearances, but it's important enough that Lakshmi packs it in her bundle as she prepares to escape Happiness House.
When we think about the purpose of dolls in our lives, the most important thing that emerges for us is that they hearken back to childhood. Often, children use dolls both in their play and to comfort themselves—so there's a certain vulnerability that comes with dolls.
When Monica gives Lakshmi "an old rag doll, loved almost beyond recognition" to comfort Lakshmi when Harish has left, it's a pretty big deal. At this point Lakshmi understands that Monica is vulnerable in ways that she doesn't let other people know about:
And I understand then, somehow, that Monica, the thirsty vine, Monica, the one with tricks to make men pay extra, sleeps with this tattered rag doll. (136.InsteadofHarish.9)
Monica might put on a brave face, but she's still soft and vulnerable inside, and in need of comfort. Consider the fact that Lakshmi thinks she has two selves, and apply the same split personality to Monica. Do we ever really get to know the true selves of the girls in the brothel? The answer may be no, but the rag doll reminds us that these hidden selves are still there.