Here are two articles that should help you:
First, how to mount web_dav from the command line (needed for the second bit)
http://hints.macworld.com/article.php?story=20020207214002198&query=mount_webdav
Then, you need to spend some time with automount, described here:
How to automount SMB shared network drives in Mac OS X Lion
And yes, I know that's SMB not webdav, which is why I posted the link about mounting webdav from the command line. You just need to combine the two articles.
Another option is to put the commands you learned from the first link in a shell script. You can then call that shell script automatically with something like ControlPlane