It sounds like a ridiculous internet rumor. But Tor.Com claims to have confirmed the casting, and a release date of 2012, with "movie studio sources." (They don't say which studio.) And Russell T. Davies may be the writer.
Update: In case you missed it, we talked to the BBC and they said there's no truth to these rumors.
The original source of this rumor is a site called PubArticles, that Tor.Com describes as an "article mill." The PubArticles post has actually been taken down, so it's impossible to evaluate whether there's any truth to it whatsoever. But Tor.Com quotes from the now-deleted PubArticles post.
Russell T. Davies is quoted as saying, "There will be brand new concepts and the film will be just as adventurous, scary and humorous as the television programme. But none of us working the film will forget what makes the character great and interesting and the long-time fans will not be disappointed because yes, the Daleks make an appearance." And the article adds that the Doctor travels throughout history curing illnesses that have been caused by aliens, including the Bubonic Plague. More details at the link.
The unnamed movie studio sources who were able to confirm to Tor.Com that Johnny Depp will be playing the Doctor in 2012 were unable to confirm any of these story elements, so let's hope that part is pure fabrication. Even with the anonymous confirmation, I'd still take even the Depp casting and release date with a major grain of salt, too. Image via Tor.Com. [Tor.Com]