How can I move my notes from one folder (gmail) to another (iCloud)?
The following worked for me: 


Go to the folder that represents the notes stored on the external server
Click Edit and choose the notes you need moved, or just swipe from the right on the individual note and tap Move
Choose the destination target and folder: either local, or iCloud


This actually moved my note from an external, IMAP-connected server to my iCloud.



The screenshot shows both On My iPhone and iCloud options not greyed out, which confirms they're both available, and the note in question is currently located elsewhere.  

But yes, it does seem like it won't let us do it the other way around, that is, move the notes from iCloud/iPhone to an external server: it simply doesn't show up in the destinations list.


  My question is: How can I move my notes from one folder (gmail) to another (iCloud)?


Seeing that most likely your Gmail account is connected via IMAP, I believe the above should work for you in the from Gmail to iCloud mode, as requested, but again, keep in mind, not the other way around. Make sure you have the latest version of the app installed.