I'm trying to compile two lists: one of music for pre-9/11 indie dads, the other of music for post-9/11 indie dads.
This isn't simply when the music was released - for example, Beck is undoubtedly music for post-9/11 indie dads, despite releasing most of his famous music pre-9/11.

Elbow are definitely post-9/11 indie dad music, as are the national. Led Zeppelin and Mumford and sons are pre-9/11 indie dad music.