Taking a full size screenshot of a web app that requires login could be supported via a cookies file. The user would log in via their browser, then tell webkit2png to use the cookies file as a source, or perhaps specify which browser's cookies to use as a source for ease of use to the end user.
Safari stores its cookies in a plist database in:
~/Library/Cookies/Cookies.plist
Google Chrome stores its cookies in a sqlite database in:
~/Library/Application Support/Google/Chrome/Default/Cookies
Firefox stores its cookies in a sqlite database in a non-guessable path:
~/Library/Application Support/Firefox/Profiles/????????.default/cookies.sqlite