An iBook G4 has a VGA port, correct?
And your Studio Display probably has an ADC connector.
I don't think you can go from VGA to ADC with conversion cables (you can go from ADC to VGA). I did find this discontinued product that performed the VGA to ADC conversion (but it's more than just a cable).
Also, I believe the iBook's video output was for mirroring the built-in LCD only (unless you used a "hack" to enable extended desktop mode). So if the built-in display has 1024x768 resolution max, your VGA output will not go higher.