When using our 1-click installer, you can choose to install in a subfolder (by typing in the folder name in the "Preferred address" field).
This way your existing site will stay visible when visiting the domain, while you can access your 1-click in the subfolder, e.g. ue-example.com/subfolder.
You can also create a subdomain and choose this as the install domain from the "Preferred address" dropdown, this way you do not have to type in a subfolder name.
When you are ready to take your new site online you can move it to the public_html folder. For most installations there are guides on how to move them from a subfolder properly. Check the documentation for the respective system.
For example, WordPress has this guide: http://codex.wordpress.org/Moving_WordPress
Article from category 1-Click installation