There's several considerations here:
1. What hardware to use?
2. What software to use?
3. Where will people see the video?
4. Data connection?
.. and possibly other issues.
The others have dealt with your hardware issues; I agree that using an existing camera might be your best option. I use an older analog Sony camcorder as my webcam at home and it kicks ass off any webcam you can buy. If you already have a camcorder on your dash it might be all you need. As was mentioned, if you have the means to connect it to your laptop already you have that part tackled. If you only have an analog output available you can still work with it; I used a cheap usb capture device and it worked quite well for webcam work.
Now on to the software. Here's where things can get tricky, and there's many ways to do this. One possible way is to use an "all-in-one" approach like this stuff:
http://www.webcamsoft.com/en/ezcast.html : an application like that can pretty well take care of most of your issues and get you up and running. They have a demo available so you can "try before you buy". There's also quite a few competing products/methods for this. The solutions I've tried before have a window on your screen so you can see what the camera sees, allowing you to make adjustments to the camera and see the resulting output.
Then there's the "who" aspect; who is your audience? They will likely need specific software on their machine to see your video, although that usually only consists of a typical windows environment including Media Player.. but its something to consider if you go with some solutions.
Now on to the hosting issue; will this be via a link on your website or through some other "community" resource? Quite a few options here. In most cases you will be sending the live video via a streaming server somewhere; this can then be viewable from other websites etc. That might require an account to be setup. This stuff is changing all the time too since new technologies are making this easier all the time. Best best is to do your own research on "live streaming video" and see what works for you.
Then there's the data; hopefully you have something good in place; video can gobble up a lot of bandwidth as you can imagine.
Hopefully this helps a bit, or will provoke some further input.