I would keep it simple.
Create a distribution group with the new alias; new.dg@123.org.
For your old.dg, if the wanted action is to send an email when someone use it; then make sure it's moved to a shared mailbox, apply the old.dg@123.org alias to it, and publish a out of office memo on it or create a auto-reply rules for the mailbox.
Please use the email address of new.dg@123.org
The problem you face is simply a DG can't send OOO message nor having auto-reply rules applied to them. You could do a transport rule to make a auto-reply but I never tried that option.
Please note you can have two email alias for one DG, but as stated you can't send your email that way.
It's why I suggest to move the old.dg to a shared mailbox.