Hi, I did a some more experimenting.
Please excuse little translation errors, I am installing in german and am translationg it back to english for more people to read this info.
It seems the debian installer is not working correct when started from SD card (the EeePC Installation docu http://wiki.debian.org/DebianEeePC/HowTo/InstallUsingStandardInstaller actually says to put the image on a usb stick and does not mention a SD card). It seems the installers CD-ROM utilities do not recognize a SD card as CD-ROM as wold be needed.
After dd'ing the CD #1 installer image to a usb stick and rebooting the EeePC it was recognized as installer CD-Rom medium.
Now the next problem arose. In the installation step "Selecting and installing software" on the tasksel page I chose "Desktop environment" and "Laptop" additional to the default selection "Base system". After a long time installing an error message apeared stating an installation error. Without any specific imformation. I think it could be an energy saving problem, which would mean the network is disabled during the long time installing (after I got the system installed I experienced automatic deactivation of the network during work which I could resolve only by reboot).
So, how did I get the EeePC installed? I booted from the usb stick, selected help to get the text mode installer (the graphic installer boot menu always hangs). Then I typed expert (so I believe install should also work) and hit return to start the installer. After configuring language, keyboard etc. I configured the network, Ethernet as well as Wlan (using WEP security) works. In tasksel in the software selection I stayed with the default "basic software" to speed up the installation. After the reboot I used aptitude to opened the taskgroup tasks and enduser and then marked the complete Gnome-Desktop-Environment and Laptop groups for installation and installed it.
After the installation was finished a reboot brought up a basic debian gnome desktop.
I found nothing EeePC specific even worse, alot of dialog boxes are too large for the 7" screen. So this installation seems to be a basis to build a usable system later but nothing a beginner would expect.
If anybody is interested to further inspect the installation problems I would be glad to assist with whatever needs to be done.
If anybody has suggestions how to configure the system to a usable EeePC environment I would appreciate any hints.
If the community is interested in further documentation in english or german I would like to help.
With the best wishes to the great debian community