I frequently create a seperate hosting account for my clients when we are redesigning their site.  That way we create a temporary URL that only we know about and can use to fully revise the site out of public view.  Then we copy the pages back to the production site that were altered at the point we are ready to launch.

 

Your host may require you to open a new hosting account with a fake domain name in order to do this, and it might cost you a couple months hosting fees for the flexibility.

 

Because I run my own servers, I have the flexibility to take that action, and tend to do this gratis for my client. 

 

Another way is to create a subfolder in your site and copy everything into that area for the redesign, but there are potential drawbacks and complications by doing this.