I would've got this on video. (don't know how, someone should explain.)
In console -
record [demo name]
When finished
stop
If you want to render the demo into video so you can upload onto youtube
startmovie [demo name] [file type ex AVI] [fps]
Example
startmovie lolololololol avi 24
It will ask you what codec you'll want to render it at. Just choose full frames.
Now you want to play your demo.
play [demo name]
Let it runs it's course. Just, try not to touch anything.
Let it render for however long. Depending on your fps in-game, and the desired FPS, it can take anywhere from 1/2 the time, to 5x the time.
Usually, if you get a solid 30FPS in-game, and are rendering a demo at 24 (Youtube's max FPS), then it would take 3x the length of a demo. (3 minute demo =/= 9 minutes to render)
Once it finishes, type
stopmovie
It will save the .avi (or whatever) and put it in your steam/steamapps/username/garrysmod folder.
Now run it through WMM, or any video editor for that matter, to get a smaller filesize for youtube.