The best you can do is what Leo said/showed.
Make sure Preferences -> Folder Tree -> Appearance -> Libraries is checked ON and it's sub option "Display under the Desktop item" is also checked ON.
Now under Preferences -> Folder Tree -> Options -> Start Folder Tree at: set to "Desktop".
This will make it look more or less like leo's screenshot.
Now if you would like to always have Dopus start in your Documents (My Documents). Make the lister look just the way you want it. With the correct Tree Item opened/selected. Then go to Settings -> Set as Default Lister. Now every time you open Dopus, it will be focused on your My Documents. And there won't be to much clutter in the way to get to your Computer drives.
At least that's how I would do it.
If you already got this looking perfect on your Laptop. You could copy it's config to your desktop to make it the same. Do Settings -> Backup and Restore on your Laptop. Then take that backup file to your desktop. On the Desktop, do a restore using that backup.
To do MrC's suggest. Type "/profile" (No quotes) in the Location/Address bar and hit Enter. In the Tree, Shift + Right-click on your My Documents folder name. Near the top of the context menu item that opens, you'll see "Root Tree Here". This will set the "Desktop" to be "My Documents" or any other folder you right-click on. The problem I see with this is that it's harder to get to your other drives in the Tree. You can still get to other drives with the location/address bar though. Or am I wrong on this? First time I played with it and my testing showed this behavior.
I personally have gone away with the Tree and made my own Tree like shortcuts to my most used folders (CCleaner Inspired). These shortcuts just get me to the roots of my most used folders. Then I would just drill down from there. This would also work with a Tree turned on.
Hope this helps.