invisbl.mdl comes with Quake. So long as you have everything set up OK you shouldn't need to do anything else with it. Likewise you most definitely should not need to be copying and pasting anything aside from the engine files around.
My normal advice with things like this is to reinstall Quake to somewhere you can easily find it later (like C:\Quake), then make sure that you can run standard WinQuake or GLQuake OK.
The next step is to try out a simpler engine. One that doesn't come with a load of extra files, one where you just need the exe and nothing else to run it. DarkPlaces is powerful, but with great power comes great responsibility, as well as a need to know what you're doing first. So let's practice with something easier before we move on to the hard stuff.
for example. Download from the "executable" link on that page and extract the zip file. (I wouldn't recommend my own DirectQ engine in this case as it will find your Quake folder and run OK, but that will do nothing to help you get DP running).
Then copy FitzQuake.exe into the same folder you have WinQuake.exe and GLQuake.exe in. This might be C:\Quake (it should be if you've followed my advice), it might be C:\Program Files\Quake, it might be C:\Games\Quake, it might be anything. If you can't find it then use the Search in Windows.
Double-click on FitzQuake.exe and it should run OK. If it doesn't work, you likely still have things set up wrong so backtrack and do it again.
Now you're ready to move on to DarkPlaces. Let's not mess around; just unzip the DarkPlaces download and copy everything
from it to that same folder where you now should have GLQuake.exe, WinQuake.exe, FitzQuake.exe, an ID1 folder, and maybe a few other things.
That should get you working.