I see what your going for. I think the client should be the one hiding stuff from the relay though, generating the noise. This also sounds like it assumes the client-relay connection is being spied on. Because I'm assuming the "relay" is using a private, recursive resolver, and therefore can't really generate noise, and would be unnecessary I think.
Discussion
if the prefix gets you what you want, then the relay has no idea what you were looking for. if not, then you can use client generated noise to hide your actual query