ok, try this. QUIT notes on the machine you're copying from. then go here:
User Library>Containers>com.apple.Notes>Data>Library>Notes.
OPTION-drag (ie COPY) those three files to your desktop. put them on a flashdrive or something (or in a folder, zip it & email to yourself).
on the NEW mac, make sure Notes is quit, and put those files in the same location (replace the ones there if there's something there).
this will OVERWRITE any notes on the new mac...
should work...