Err just no. First of all there is a lot more to running the factoring method on a quantum computer than getting enough qubits (right now you need more than 1000). You need to keep it coherent for the many many operations that have to be run on it. Also building a QC is exponentially difficult. It is not like "just add a qubit" adding a single qubit to make 3 qubits is on the order of 2x harder than 2 qubits. Going from 100 to 101 qubits is again 2x harder than the 100 qubits. You get the idea.

So even if they can make a few 100 qubits your still totally safe. Unlike classical computation there is no way to use a 100 qubit QC to solve a problem that needs a 101 qubit register. And right now with decoherence time we are getting, you also need many many many extra qubits for error correcting.

Finally if there really is some uber breakthrough and +1000 bit QC become reality, there are public key schemes that are not compromised with QC. The keys are fairly big, but on the modern internet this is much less of a problem these days.