Added the most primitive possible Import/Export feature that addresses the basic problem. It consists of a text area and two buttons at the bottom of the window. Scroll down to find them.
The export button dumps the JSON data structure into the text area. You can copy from there to an email and send it to yourself or a friend, and paste from the mail into DunGen there and hit Import to load up the dungeon.
You can edit a bit on the field to experiment with things like colorizing edges and nodes. But be careful not to break the data structure if you want to import.
After importing, give it a name and save it to your browser's local storage to access it again.