Yes, Dark Knight is finished. The problem is we already know the ending now. Either he's in Arkham or he was killed or vanished. There will not be a second appearance by the Joker in this series.
Unless Jack Nickelson returns *crosses fingers*
Or more realistically, they will just replace the joker with another actor like they have with Rachel (for those who don't know, Maggie Gyllenhaal has replaced Katie Homles). There is no way that Jack Nicholson will be brought back in. Just impossible. Don't get me wrong, I like Nicholson's Joker, but Nolan is going for a more realistic portrayal of the Batman franchise now.
Anyway, with such a large array of Batman villains, I think they should just peserve Ledger's Joker because a lot of effort and determination went into playing that role. It wouldn't be right to just replace him with another actor in the third film. They should just make two-face the main character and add another villain like catwoman or the riddler.
Either way, it's sad news about Ledger. He seemed like a really nice guy. I feel sorry for his ex and daughter.