I moved to Oregon from Southern California three years ago. I believe what you propose will work. Your daughter will have to title and register the car in Oregon. Your name can be on the title as co-owner. The car will have to be VIN inspected at a Oregon DMV office before proceeding with title and registration. You don’t need inspection at the nearest DMV, or even in Multnomha county. I would choose an appointment office in a small town reasonably close to your daughters residence. Quiet, easy parking, friendly service. The Oregon DMV website is pretty straightforward with the instructions.
In forty years living in California and playing with very old, sometimes odd, European cars, I experienced that California vehicle code was sometimes so complex, the DMV employees didn’t know all applicable department processes, and form sequence. I haven’t found that situation at all in Oregon. Currently inspections are by appointment only, the state government is very serious about C19. Inspection appointments are several weeks out at this time, but just a easy five minute process on day of inspection. Insurance won’t be on your current policy, your daughters address and name must be used. You can be listed as co-owner on the policy as well.