It looks like the Sony Xperia J Android 4.1 Jelly Bean update is now available for the handset, the update has been released as an over the air update and it comes int the form of Android 4.1.2 Jelly Bean.
The Android 4.1.2 Jelly Bean update for the Sony Xperia J brings the firmware on the handset to versions 11.2.A0.21, and it brings a range of new feature to the device.
The update should be available for the Sony Xperia J as of now, and you can check to see if the update is available for your handset via the setting menu.
Source Xperia Blog
