Just install the new JDeveloper into a new directory.
Backup your workspace/project
And then open them in JDeveloper 22.214.171.124 - this will migrate them to the new version.
Note that once a project is migrated to the new platform you can't go back - this is why having a backup of the 11.1.1.* version is important.
Read the migration section here: http://www.oracle.com/technetwork/developer-tools/jdev/11gr2update3-1851251.html
To learn what JDev will do when moving to 126.96.36.199