Streaming from laptop to Internet

I browsed through and didn't see a thread addressing this, so please forgive me if this is a dupe.

Here's the situation:

I have an HD webcam and an audio source plugged in to a laptop that can run either Windows or Mac. I want to stream that audio/video signal to a server, where people can view it from a web page in a Flash player, much like they would play a YouTube video. There may be a dozen or so viewers.

I came up with the hare-brained scheme of running ffmpeg to stream the sources to an RTMP server that I set up running Red5, then creating a web page that uses Flowplayer to connect to that Red5 server and provide the Flash player. This just seems *really* complicated, and I wonder if there's an easier way to do it.

This is a one-time event, so we're not looking to invest five figures into a streaming setup, but we're also not opposed to spending a little money on a service that can make this easier.

I appreciate any input in advance!