Amazon has opened their KDK Beta program. Amazon also published a KDK FAQ. As suspected, it’s Java ME based with a custom API for the Kindle:

[It will] provide UI components, JSON and XML parsers, HTTP and HTTPS networking, secure storage, and other features. Other APIs like audio and dictionary access will be available in a future release of the KDK.

Development will be possible in an Java environment, but it appears that Eclipse will be supported more directly.