I'm not too clear on WP works in this regard, but if it is generating absolute URLs on things like images, I would expect that it would update all this when you move the site to a different domain. There is probably a config file where you specify the site URL. It's common to move a WP installation like this (e.g. when people build the site on a development domain before going live) so it shouldn't be hard. I believe there are some plugins that can help with moving a WordPress site to a new domain, too.
Here are some links I found with a quick google search ("move wordpress to new domain"):