That was my unserstanding, but it's not the case. I've managed to list all the indices on the principal and there a quite a few missing on the mirror (maybe mirror isn't the right term?). I'm not sure what the setup is but surely this can't be right?
More likely you are using replication. If you were mirroring you wouldn't be able to read the replica as it's in a restoring state. You'd also see "Mirror" in Management Studio next to the database name, plus the status (Synchronized, Synchronizing, Disconnected).