In FF on the laptop, go to Bookmarks -> Organize Bookmarks
In the window that opens, click Import and Backup, then Export HTML (file will be called bookmarks.htm) to your desktop on the laptop. Then copy this file to your new desktop. If the laptop and desktop are networked, this will be a simple copy over. If not, sneakernet is the next best option. i.e: use a USB thumb drive.
Once you have the exported bookmarks copied over to the new desktop (or the thumb drive plugged in and recognized), open FF on the desktop, then Bookmarks -> Organize Bookmarks. Then click Import and Backup, then import the bookmark.htm file. That oughta do it for you! And they will be organized exactly as they were on the laptop, you shouldn't have to do anything else unless you want to.