The problem is that you seem to target a specific kind of people that might think like me and not immediately provide a referral link on the FB/twitter/whatever profile to have as many people as possible to signup for.
Anyway, I love the idea, this kind of shirts are 90% of my current clothes so I'll signup for it right away.
What prevents you from trying with ONE design first and see how it goes? Maybe rely on another t-shirt design shirt for your first go? In France http://www.lafraise.com/ is pretty well-known or websites like teefury.com could be a good start!
How will you handle fake accounts and people trying to game your system? Most of the time, the 1$ incentive is tied to "someone signing up AND ordering something on the site" first, no?
EDIT: Some additions, the email you send right after signup is nice but I think the first part should be on your website! It describes clearly who you are, why you're doing this project and also why your design would really be better, it would be great along with your examples.
EDIT2: Why not have part of the website already done? I have to "pretend" I sign up in the launchrock page to know wether anyone used my referral link? Why not have a "normal" login system and a detailed page where I can see who accepted the referral link? To avoid spending too much time on the websites first you could use something like www.dailycred.com to handle signups properly (this was shown on HN a few weeks ago).