Unclear what exactly you mean. WebDAV is a document store interface (essentially) that runs over HTTP, and has nothing to do with authentication, though usually it will be behind some other HTTP-level authentication scheme.
It is not a producer of streamed data. Also, while you can mount a volume over WebDAV, I don't believe that you can effectively tail or stream a continuously updated log file. (It would depend on the WebDAV client, and even so I suspect it would be rather inefficient.) It is similar to FTP in this way. The client is not part of Splunk, but usually would be a utility in the OS.
So if there is a file somewhere that is accessible via WebDAV, I believe you would handle it the same way you'd handle a file that is accessible via FTP,using a scheduled script. You can experiment with mounting it as a volume in your OS and attempting to use "monitor". In both cases, the authentication would be handled outside of Splunk by the webdav client you use.