Regenerate the top part.
The splitting doesn't actually kills the doll - just its bottom half.
The bottom half becomes a nest for the little doll that was gestating on the inside of the "mother doll" for a bit, until it can go around hunting for cookie crumbles for itself.
The upper part, on the other hand, shrinks a bit in size and regenerates. After some time passes, it can produce a new doll on its now-empty insides.
This way, the doll population will increase steadily, as most other living beings. They would only truly die from old age, predators, accidents or kid-induced acts of doll terrorism.