Moving store to new domain name

I want to change the domain name of my zencart website (Both old and new domain on the same server).
Is there an easy way to just move everything from the old to the new domain name and have the new domain running seperately from the old domain (So that I can delete the old domain) but still have everything for sale still working.

https://www.zen-cart.com/content.php?142-i-want-to-move-my-zen-cart-installation-to-another-host-or-a-different-server

Are you planning on dropping the old domain name immediately? Since you are staying on the same server, you might just do a 301 redirect. If you have cpanel for your account, it's fairly simple. You can also add something that will tell those coming from the old domain that it has changed.
After a time you decide on, you just remove the redirect from the old domain and let it lapse.

Are you currently with a host that provides cPanel and moving to one that also provides cPanel?