I dumpster-dove a trailer for a bike that looks to be functioning, minus one wheel. Here's a picture of the quick-release block on the bike, and then the wheel. The rubber says "KENDRA 46-407 1.75x20", but I haven't had luck in finding a replacement wheel.
From the looks of it, the black gear-thing is built into the wheel, not an add-on.
Larger images can be FOUND HERE.
Thank you for the help!