There are several options available regarding where and how you will construct your new web site.
Based on the fact that you want your test environment to be exactly like your production, you should opt to create your new web site on your production web server. However, that may not be practical in all cases. If your web site consists entirely of static HTML pages, this is not a problem. However, if your site contains pages that, for example access a database, it is better to test them on a test server. In this case, it is important that the test server/environment be as similar to the production server/environment as possible.
Note: if you are using a Mac, the test server could be your Mac.
As you begin to create your new web site, your first instinct may be to create a newsite folder in your current site, and start creating your updated site in that location. This is probably not the best approach for a number of reasons. First, you want the structure of your test site to be identical to the final production site. If you are in this subdirectory structure everything is one level down, which means you will have trouble getting any absolute path reference working correctly. You may already have a Dreamweaver site configured to your current site. While Dreamweaver will let you configure a second site to a subfolder, it warns that things may not work correctly.
For the above reasons, it is best to start building your new site in a parallel folder to your current web site. You will need to have your system administrator set this up for you. If your current web site resides in a folder called xyzdept you may wish to request the creation of a test folder for your site called something like xyzdeptclf.