It would be better (and more reliable) if you did have a proper template override in place, but the following may work
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FTP your entire ZC installation (all files and folders) to your local drive.
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Create a database (empty) on your new server (domain).
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FTP a fresh copy of ZC 1.3.8a to the new server and perform a standard install.
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What you do now depends a lot on what additional modules you may have installed on your original site, because some of these modules do the following:
- they create new files
- they modify some existing files
- they create new folders
- they create and/or update database tables.
So you need to establish what modules you have, and (very important) which of the above alterations/additions such modules may be invoked on a new site.
Once you have established this, (and depending on the modules concerned) you will have to:
make appropriate updates to your database
identify altered files and their path locations
identify additional folders and the relevance of their contents to a new install
... and then ensure that these files/folders are sent FTP to the server.
Remove your includes/configure.php file from your local drive (put it in another directory away from these files and folders) then FTP your includes folder (from step 1) to the new server, choosing to OVERWRITE all files and folders on the server where you've just installed the new software.
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You now need to edit your two configure.php files (in includes and admin/includes to reflect the new server URL and associated paths, new database name, new database username & password, etc...
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Your will need to run fix_cache_key.php (see free addons) to re-set your database cache location.
However, it may be easier to clone everything (files AND database) so that the integrity between your code files and your database set-up is consistent. Before your cloned site will work, you'll still need to edit the two configure.php files as described above and run the fix_cache_key.php .
Then its a case of cleaning out the database of all unwanted data - probaby just product and customer related data.