Scrum doesn't propose a methodology that eliminates QA. Scrum actually says very little about development or testing since it is actually just an adaptive project management methodology that can be applied to ANY industry. The various roles and responsibilities throughout a software company shouldn't change that much if the only change you are making is adopting Scrum.
I am a tester on a team that switched to Scrum almost a year ago. I still have the same role and general objectives that i had before. What changed was how i accomplish them. There is no longer a Dev team and a QA team. Now there are just Scrum teams, with dev and QA integrated into the same working group. I do my testing inside of a sprint, and my tasks are managed and tracked in the same way dev tasks are. This is basically the same as the two posters above me mentioned.
Like you said: "The Scrum team(s) will be in charge of the testing and it's their responsibility that whatever comes out of the Sprint, is fault/error free." QA's role is to verify this and provide feedback on the product.