Dreamweaver is a very powerful tool and is built in with comprehensive set of features to accomplish this task.
You need not really worry about relative URL's unless you have some .htaccess/ similar server-side configuration where you've modified certain aspects of how your server renders these files on WWW
For absolute URL's, open Dreamweaver, Site > Check Links Sitewide
This will bring up Link Checker on DW. You could filter the links to show broken links, External links or Orphaned files. Sort it by 'External Links'. You'll be able to see all external links which are absolute URL's as you've mentioned in your post. You could just click on the URL and modify it to the new URL for your external absolute URL.
GoDaddy - you need to decide if your redirect is a Permanent one or a Temporary one. If it is permanent, you'll be doing a 301 redirect, notifying of all search engines and hosts that your old domain has permanently moved to the new one. If its a temporary one, you'll be doing a 302 redirect, notifying that this is only a temporary redirect. Either way, this link should help you: http://support.godaddy.com/help/article/5120
Let us know how it goes.
Thank you for your advice. This was very helpful.
I have just completed and uploaded my new site, www.sagelaw.us (which replaces websage.us).
I used the Ennergi template from Project Seven Development. I modified the styles substantially for my own preferences, and I learned a great deal about CSS and my new Dreamweaver CS 5.5 in the process. (I had been previously using Dreamweaver 8.) The power of this program and CSS are very impressive. Consequently, the changeover was relatively easy and efficient.
Thanks again for your help.