This would be out of the scope of DAVdroid. DAVdroid is a sync adapter between Android and CalDAV/CardDAV, nothing more.
Did you already search the stores? In a quick search, I have found Copy Events which looks like what you need?
I have some read-only calendars on my server (ownCloud). If I attempt to add a new calendar item on the phone, DAVDroid fails to sync that calendar. Could DAVDroid detect that a calendar is read-only and mark that somehow so it is impossible to add items to that calendar? Or is this a problem on the server side, with ownCloud not tagging the calendar as read-only properly?
DAVdroid detects read-only calendars and marks them as read-only in the Android calendars provider, i.e. calendar apps should not be able to add events to these calendars. However, this detection is done when the local calendar is created, which is when you add the account.
Can you please delete the DAVdroid account, add it again and see whether the calendar has a “read only” icon next to it? In this case, DAVdroid has detected that the calendar is read-only and should mark it as such.