While I'm not in total disagreement with the previous response, I would not be so quick to say the existing PQRs would not support a WPS for ASME Section IX. A thorough review of the existing PQR as well as the base metals used and the filler metals is in order first.
Assuming the base metal met both ASME and ASTM requirements, e.g. A36 versus SA36, and if the filler metal used met both AWS and ASME requirements, e.g., AWS A5.1 versus SFA 5.1 (most do), the essential variables of D1.1 are more inclusive than ASME Section IX. It is possible to rewrite the PQR to include ASME nomenclature and Section IX as well as the additional restrictions imposed by the appropriate construction code.
If the question was whether a procedure qualified to ASME Section IX could be adapted to AWS D1.1, I would say no, because the essential variable commonly omitted by Section IX are required by AWS D1.1, the test plate must be examined by either RT or UT for AWS (not required by ASME), and the bend test results are more stringent for AWS than for ASME Section IX.
Best regards - Al