I don't think you're going to find a climbing carabiner that small. The ones I have (not that I climb any more!) are more like 4 inches for the smaller non-locking ones. The metal diameter is a little less than your pinky finger. You would have to put a 1/2" (maybe 3/4") split-ring on the key and then clip the split-ring to the biner.

Have you thought about something like this instead of a biner?

http://countycomm.com/ring.html