Sure! There are several ways to approach it, depending upon your comfort level in the shell and editing files, whether you are running WordPress from within a "yourdomain.tld" directory or a "yourdomain.tld/subdirectory", and whether you also want/need to change the database that WordPress uses.
There is an excellent guide to "Moving WordPress available on the WordPress codex, which provides step-by-step instruction for various types of moves and explains the issues involved. I think it does a far better job of walking you through this that I am likely to be able to do.
If you are comfortable in the shell, the easiest way to do it is just to move/rename the directory that holds WordPress to another and edit the configuration file (you also have to do a few other things, like rebuild permalinks, etc.,) You may, or may not, want to also create another DB host to hold your data, but you don't have to do this.
Essentially, you just need to have the directory that hold WordPress accessible from the new domain - the panel can help you do this by "editing" your domain set-up, or you can rename/move dirs. In it's easiest form, your WP is running from the "base" directory of your domain, but there are variations of that if you are running it from a subdomain.
Alternately, you can certainly move it using the process described in the link I provided above.
If you want it be continue to be a "one-click" installation so that you can use the "one-click" upgrade process to keep it current, you will need to actually recreate a "one-click" installation on the new domain, export your data from the old one, and import it into the new one.
You create the new "empty" WordPress on the new domain first (just like you did originally), and the instructions for how to do that "exporting" and "importing"are in the guide I've already referenced. Make sure you have first updated your "old" blog to the same version as the "new" one-click installed version will be before doing this export/import dance - things will go a lot smoother for you if you do.
I suggest you give that guide a thorough read, and give it a try. Make sure you don't skip the "backup your data" steps (in case something goes wrong). If there is something you just don't understand, or if you have a particular question, post back here and I'm sure one of the "WP wizards" that hang out here can give you more help. GOOD LUCK!