How to transfer/copy Notes from one iDevice to another without using restore method?
With iOS 9:

Open the Folder containing the Notes you want to move.

Click the Edit button. It is faint. You might not see it right away.

You will see a column of selection circles ⭕️ appear, and also the words Delete All and Move All.

Tap the circles for your target Notes, then Move To ..., and the destination.

All done.