2manybikes, I realize your post asks specifically about
making a trailer, but if you decide to go the purchase route, you might look at these guys:
http://www.xtracycle.com/
Another commuter here at work is having them build a "sport utility bike" (that's their term for these trailered bikes) for him. He hasn't received it yet so I don't know how good their stuff is, but their web site shows pictures of dogs riding on/in their trailers.