Uncomputing measurement gate?
You seem to be under the impression that we need to measure a qubit in order to copy it. That is not the case because the copy operation is performed by the mapping $|a,b\rangle \mapsto |a,a \oplus b\rangle$ which, when $b = 0$, can be realized by a CNOT gate. There is no measurement involved at all. You only need to know how many ancilla bits (i.e., initialized to zero) you need beforehand so as to have an adequate quantum circuit size.