Yes, both movies The Hobbit will be filmed at the same time. This will help maintain continuity for both films and ensure the actors are available for the entire filming process.

The release dates were originally publicized to be December 2011 and 2012 with filming set to start around March of 2010. However, delays due to finalizing the script, MGM’s financial woes, finding a new director after Guillermo Del Toro stepped down, and an actor’s union boycott, have pushed the release dates to 2012 and 2013. The films were officially ‘greenlit’ (given the go-ahead to start spending money on things like sets, locations and actors)  on October 15, 2010 with filming set to begin in February, 2011.

Useful Links:
Hobbit ‘greenlight’ announcement

In a nutshell: no. In the early stages of their collaboration, PJ and GDT planned to film the events in the book The Hobbit as a stand-alone movie, with a second movie, or ‘bridge move’ as it became known, used to address events outside of the primary storyline of The Hobbit, continuing to where the Lord of the Rings movies pick up the story again. Fairly early on, however, they confirmed that it made much more sense to film the storyline of The Hobbit over the span of two films, addressing events outside the story at the same time. ill span both films. PJ: “We just decided it would be a mistake to cram everything into one movie.”