Unfortunately, Gmail/Gchat does not currently support this. To do this, you must use a client such as Gtalk.
As per Google's instructions, you can share your current music via Gtalk:
If you'd like to show your contacts what music you're listening to at that very moment, select Show current music track from the Available or Busy section of your status drop-down menu.
Your status will automatically update each time your supported music player starts a new song, listing the track name and artist information:
If you stop your music, your status will display the default Available or Busy message.
The list of supported players is located here.