You see, the finder is divided into two parts. The left side is defaulted with Applications, Documents, Music, Movies and Pictures. You can't move those icons anywhere cause they are Virtual aliases. They don't exist as files.
To drag something in the dock, you need to drag something from the right side. So if you want your Music folder to go into the dock, your most basic method would be to go to the "Home" folder, and then drag "Music" from there. Alternatively, you can click on Music folder in the left sidebar, and in the title bar, there will be a small little icon. That is a live icon. Just drag that down into the dock and it will create a stack.
Btw, that icon is there in a lot of other apps as well. So if you want to save your MS Word document onto an external drive, just drag that icon from the word title bar onto the external drive and it copies it there..