When should I design my first website?

There are some references to 960 gridsystem in the CSS deep dive, if I remember correctly, but I would recommend that you hold off on frameworks like these at first. As for when the "right time" is to design your first website, to quote the guys on Shop Talk: "Just build websites!"

The right time is now. Maybe you should finish the HTML and CSS deep dives, but then you should go ahead and put your new knowledge to practice. As you go, you'll find some things you don't quite understand - and that's OK...take that as another opportunity to do some more searching, or get back into the lessons to clarify something. You will ultimately get out of this what you put into it. So get to coding as soon as you think you've got something to work with. :-)

There's no clinical point in your learning to start. Just like you'll never finish learning. There's always new things to learn, new challenges to beat, new ideas to implement. If you've got a good handle on HTML and CSS then open up the text editor and either start to recreate a site or, if you have an idea, start on that. Just be prepared to throw it all away on a regular basis and go into it as version one of many. As you learn new things, you'll soon start to find better ways to do things that fresh starts will help with.

I know when I was learning, I've done about 10 versions of the same crappy thing. I have designers do my design work now but even so, I still do two or three versions to perfect functionality and tidy things up after I've been chopping and changing in the development process.

I'd start building one now, if you want. Keep building up on it while you learn with the Treehouse videos.