A plugin like Duplicator or something similar would make it pretty easy to accomplish setting up a duplicate installation. That said, it’s not strictly necessary to get all of the existing data across to the test installation, at least initially.
For troubleshooting purposes – if you don’t or can’t use a tool like I just mentioned – your new installation need only contain copies of The Events Calendar and Events Calendar PRO. Create some test data and see if the problem pops up under those circumstances – then start adding all the different components that exist on your live site and see if the problem shows itself again. If it does not, then we could look at pulling across the actual data (or making an exact duplicate that includes the same data, etc).
Does that make more sense?