Possible to move scheduling from one site to another?

I am working to scope out a project for an existing squarespace site that has been custom coded. I am redesigning in a demo site and once the redesign/structure is complete, I would like to just point the domain to the demo site. My roadblock is that the current site has scheduling and we need it exactly how it is on the new site as well.

Would I have to re-build the scheduling in the new site or is there a way to move their entire booking system to the new demo site? They are a medical spa with a ton of services and multiple calendars and locations so I would rather not have to rebuild that. 🙂 TIA!