We're planning on redirecting her quick links to new folders on the external drive, but I'm wondering if I can tell dropbox to continue backing up her Documents, etc. from the external HDD?
That won't be possible. Dropbox can only sync one location; wherever the Dropbox folder is located. It will not sync folders located outside of the Dropbox folder. Even the backup feature works by moving the Desktop, Documents and Downloads folders into the Dropbox folder.