As has been previously stated, primary development on DA1 was completed at the beginning of 2009. The PC version was originally slated to ship around March or April, but EA held it back for a simultaneous release with the console versions, the porting of which continued until the release in November 2009. That essentially means that there will potentially have been up to 2 years available for development of DA2 by the time it ships in 1st quarter 2011. Now judging from what devs have said, they didn't leap into developing DA2 straight after primary development work on DA1 ended, but I am fairly certain that they started at least some initial work on it before DA1's retail release. If you look at the credits for Awakening, released in March 2010, you'll see that it was pretty much developed by a "B team". The obvious explanation now for why that was the case is because the bulk of the DA1 "A team" was already at work on DA2. This is also supported by the original post in this thread, pointing out that some copies of Awakening shipped with teasers for DA2.
Also keep in mind that, again as has been previously stated, contrary to what Quanon said DA2 is not using a new engine. It's still running on the Eclipse engine and from what they have shown so far there don't seem to have been any significant changes made under the hood. They've changed the art style, but that is mostly cosmetic.