currently I am running my gallery as a subdomain...... I just recently purchased a new domain name so I can run my photography website separately. It is still under the same host, just has to be in a new directory..
coppermine currently is installed like this
/public_html/subdomainname
and I want to move it to
/public_html/newdomain
will this work or will I have to reinstall coppermine and enter ALL my settings/albums/photos again?
You can do that just fine - Coppermine only stores the relative path, not the absolute one. You will only have to reflect your changes in coppermine's config by changing the gallery URL. See http://coppermine-gallery.net/demo/cpg14x/docs/faq.htm#moveGallery