Yes there is a method for moving.
What you do now depends upon where you are with your 1.3.x install.
Did you do a fresh install of this already?
If yes, have you made many stylying changes and are they in your overrides areas?
If you are at a point where you can begin again without losing much.
copy all of your current zen files to your PC. Backup your current DB to your PC.
Then FTP the cart files to your new location.
Determine your current DB name, user, & pass(in the configure.php) Write this down.
Create a new DB and name differently than other as you are on the same server.
Add the same user and pass to the new DB. restore your DB backup to this new DB.
Now on the copied store locate both configure.php files and at the top portion of the file correct the path to this store from https://www.oldstore.com to https://www.newstore.com
At the lower portion of these files find the DB information and change the DB name(if you assigned the same user and pass this can be left as is) save these files and upload to their correct locations.
This store should now function.
Install 1.3.x and it will detect the previous version and upgrade.
do what you want for styling.
