I doubt you will find much in Danish records, as despite your ancestors' Danish heritage, they were German residents when they emigrated, as indicated on the passenger list, and the childrens' births were likely recorded in Germany.
For a review of the area's confusing background, click on the History tab at bottom of this website, and note especially 1864:
http://www.rootdigger.de/There are a few Klodts listed under the Emigrants tab, but no indication of villages they came from.