Your contacts.xml is empty (see https://github.com/rfc2822/davdroid/blob/master/res/xml/contacts.xml)
Consider using my proposed one to enable all fields (like birthday, which is not enabled right now).
Proposed for davdroid: https://gist.github.com/dschuermann/6954672
Also see this example from Google: http://grepcode.com/file/repository.grepcode.com/java/ext/com.google.android/android-apps/4.0.4_r1.2/packages/apps/Contacts/tests/res/xml/test_basic_contacts.xml?av=f
