To answer your question - no, you cannot point to a domain and host.
You must either a) host the stream yourself or b) pay someone else to host it for you.
If you plan on hosting it yourself, a static IP address would come in handy.
Keep in mind that your bitrate and number of listeners is limited to your upload bandwidth
and by "yourself" I mean effectively off your home computer.
For help see the following URLs:
There's pretty extensive documentation available on the Shoutcast Website:
http://www.shoutcast.com/support/docs/
and the forum
http://forums.winamp.com/forumdisplay.php?forumid=140
Other great resources are:
Oddsock
http://www.oddsock.org/
and the forum
http://www.oddsock.org/openbb/
Casterclub
http://www.casterclub.com/
and their Forums
http://forums.casterclub.com/
SpacialAudio (down?)
http://www.spacialaudio.com
Alternately you might consider looking in to Peercast:
http://www.peercast.org
Shimone/Justes
http://www.staticbeats.com > Electronic Music > Digital Culture
http://www.boomboombap.com > First Come > First Heard