Are Alice and Bob allowed to copy qubits in quantum communication complexity model?
Let me add to Artem’s nice explanation a pedantic point about your wording “something a quantum algorithm cannot do.”

In the usual setting of communication complexity, each party is allowed to perform any local operations, regardless of whether it is computable or not.  This is true in both classical and quantum cases.  In this sense, each party is indeed allowed to do something a quantum algorithm cannot do.  However, Alice and Bob are still constrained by the law of physics, and cloning is disallowed because of this.  In short, cloning is disallowed not because there is no quantum algorithm for it, but because it is ruled out by the law of physics.