At this time, Squarespace does not support such a duplication or transfer of content from one Squarespace site to another, despite offering a limited data export feature.
There are two options that you may attempt, both a little rough, and neither guaranteed to work:
1) You may attempt to export for Wordpress, then import from Wordpress using the XML file you exported.
- Settings > Advanced > Import/Export > Export > Wordpress > Download
- Settings > Advanced > Import/Export > Import > Wordpress > Advanced > XML Export Upload (add exported file)
- Then reassemble the pages into a parent/child relationship, add missing settings and images, etc. There will most certainly be errors and missing data from the import.
2) A developer (not associated with Squarespace) has developed a plugin (not free) that does allow the duplication of pages between sites. It is a third-party solution, not supported by Squarespace.
Note that, using this tool, it is my understanding that you would not be able to duplicate the index page/folder and its sub-pages in a single action. Instead, you'd have to create the index page/folder in the new site, then individually duplicate each child page within it. Once all child pages were duplicated, you could then move them within the manually recreated index page/folder.
You may also consider submitting a feature request to the Squarespace Customer Care team.