2 websites 1 hosting company Questions

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I have one install of concrete5 with a hosting company with a domain name of: test1.com
The company would like to mirror this site and make a change to the logo only for a second domain: test2.com
What is the easiest way to to do this?
I was going to install concrete5 to another directory and point second domain to this location.
Can I just copy first website content to this location so I do not have to rebuild?

This is the first time I have had this request so anyone with experience in this type of installation please let me know your thoughts.

Thanks so much!

John