Here's some great bit of news! Turns out Nick, luckily, haven't forgotten Korra completely, and have announced the release date of the Book 1 DVD and an art book:
The release date for the Book 1 DVD is 21st May 2013 on Amazon, and is currently priced at $15.99. With no official word from Nickelodeon so far, though, the date should be seen as tentative at best for now.
The Legend of Korra: The Art of the Animated Series (Book One: Air) will be released on the 24th July this year and is priced at $34.99. The art book of Avatar: The Last Airbender offered not only beautiful artwork and designs from the Avatar universe but also great insight into the whole creative process behind it, as well as giving some minor details about the characters not shown in the show (like how Combustion Man lost his limbs), so I'm excited to see what the new book will have to offer!
While on the subject of Dark Horse publishing Avatar material, it seem that information on The Search - Part 2 also got an update, including cover art:
While it's very unfortunate we have no confirmed Book 2 air date so far, at least we'll still have these until the time comes!
Edit: Amazon have apparently removed the date from their pre-order page and marked is as till to be announced, so it’s really up in the air at this point. Thankfully all other release dates I mentioned still stand at this point, though.