While Scrum is easy in theory and hard in practice, I wanted to hear your definition of Done; i.e. what are the gates (unit test, code coverage > 80%, code reviews, load tests, perf.test, functional tests, etc.) your product has to go through before you can label the product "Done"
I'd say it is up to your team to decide. Talk with the product owner. Ideally done would be when a story is in Production and being used. However, there is a time gap between when a story is development complete and in Live. Makes it hard to track how long a story took to develop.
In my team, our definition of done is, when the developer completes a story,and does a "show and tell" to the rest of the team(testers, product owner), and if everyone is happy it goes into the subversion trunk.
Further testing is done off a automated build from trunk.