IMHO, the simplest way to do this will be to add an FTP server (really less painful than it sounds) to the desktop.
First a couple of questions. Do you know if your router is using DHCP to assign your desktop and laptop an ip address? You can find this out by typing at the command line
ifconfig (you might need to be root). Look at the output for eth0 and see if you see a phrase like
inet addr:192.168.1.2. If you do have an address like that on each computer, then make note of the address of the desktop and from the laptop type
ping -c 3 192.168.1.2 (or whatever address it is). If you get a good response, then you're set to install the FTP server.
I haven't used Suse in a while, but you should be able to go into Yast and install vsftpd or proftpd (not sure which is on suse) on the desktop. Once it's setup, you should be able to go to the desktop and type
nmap localhost, which should show ftp on port 21/tcp.
Now on the laptop you should be able to open konqueror and in the address bar type
ftp://192.168.1.2 (or whatever address the desktop has) and it should prompt you for a username and password. Then just navigate through the directories and transfer files.
Come back here if you're still having problems...
