The webdav.service file below advertises the path to some WebDAV share. The string:

/webdav/path

has to be replaced with the relative path of the shared folder over WebDAV.

webdav.service

<?xml version="1.0" standalone='no'?>
<!DOCTYPE service-group SYSTEM "avahi-service.dtd">
<service-group>
  <name replace-wildcards="yes">%h</name>
  <service>
    <type>_webdav._tcp</type>
    <port>80</port>
    <txt-record>path=/webdav/path</txt-record>
  </service>
</service-group>