I prefer not to invent new variables when they aren't strictly
necessary. org-directory is one such variable (although the other path
variables are still necessary).
The config/private module has been removed. ~/.doom.d (or
~/.config/doom; whichever is detected first) is now a first class
citizen of Doom and should just work(tm).
Your init.el only needs to contain:
(require 'core (concat user-emacs-directory "core/core"))
And you may place your doom! block in ~/.doom.d/init.el (or
~/.config/doom/init.el).