I though Carr was signed through 2007 at least. There is an article on ESPN talking about the recent youth movement in general and they say his contract is up in 2005. I posted the paragraph below because it's about halfway down.
The only downside to this seven-year quarterback bonanza is what happens when these young quarterbacks reach the end of their contracts. David Carr's contract ends in 2005. Tom Brady, Michael Vick and McNair have to renegotiated in 2006. Jake Plummer, Kyle Boller, Rex Grossman, Plummer, Brooks and others are signed through 2007.