Testing Newer WordPress on Different Server

We’re running WP 3.1.3 and are now able to upgrade to 3.5 (finally). The issue is that we need to test the new version on a separate development server, and from what I’ve seen if I copy the database to our development server, the posts and links will be relative to our production 3.1.3 server. Is there some way I can copy our current 3.1.3 installation to our development server and have the posts, pages, etc. function properly? Thanks.