Hello,
For contacts: did you try Copy Contacts? I don’t know whether there are apps for moving calendar entries, but I guess so.
You can also export all contacts/events and then import them again into the DAVdroid account (works at least for contacts, but I’m quite sure that there are calendar apps which support import/export).
I understand the necessity of this feature, but it shouldn’t be implemented in DAVdroid, but in a third-party app, because
it’s not related to DAVdroid (you might want to move events/contacts between other apps’ accounts, too) it’s not part of the CalDAV/CardDAV synchronization, and DAVdroid should be kept as simple as possible.