How can I put my music on dropbox without moving the iTunes folder
The easiest way to this would be to simply create a folder in DropBox and then create a Symbolic Link to your Music only folder in iTunes.

There is a useful article on symlinks available here. Another one specific to DropBox is available here.

In example you could create a symbolic link to a folder named Music in DropBox as follows:


  ln -s ~/Music/iTunes/iTunes\ Media/Music ~/DropBox/Music