Primarily this short piece is to re-enforce the fact that the softer, kinder Jackie was a future version of her. This is the Jackie who nags The Doctor about his relationship with Rose. It is also him rebooting their romantic relationship after erasing her memory of them declaring their love for each other. He is taking it slowly now. Singing a romantic song to her, trying his best to placate her mother. And itís going all right until he gets an emergency message.
Christopher Eccleston, aka the 9th Doctor DOES put singer as one of his talents on his resume. The only time most of us have heard him sing, however, was on the ITV 50th anniversary special when he sang the theme tune to the Muppets.