Sarah Jane feels the effect of the rumours before she actually hears them. It's common knowledge amongst her alien associates that she is a friend of the Doctor's, so the first sign that something is wrong is they all begin to handle her with kid gloves. By the time the tale actually works its way round to her, she's mostly worked out what the story is. The Doctor is dead, they say. Really and truly, this time. A fixed point, no undoing it. They say he faced death with dignity, without railing against the inevitable.
She knows better than to believe it for a moment. That old rascal's spent too much time defying death to give in gracefully now. Besides, he as good as promised her she would know when the time came. That she'd feel it.
Sarah Jane knows the Doctor isn't dead, no matter what the rest of the universe believes. But that doesn't mean she won't be keeping an extra sharp eye on her particular corner of it. Any enemy of the Doctor who thinks Earth is easy pickings now he's supposedly gone is in for a nasty surprise.
She'll see him again, one day. Ever since Deffrey Vale, she can hardly get rid of him. Until then, she'll fight on in his name as though he truly were dead and gone. After all, he'd expect nothing less of her and she's no intention of letting him down.