You can use the xrandr tool to control what gets displayed where.
If you don't have it on your system (/usr/bin/xrandr), you can get it with:
yum install xorg-x11-server-utils
For xrandr, your Eee screen is called LVDS, and the external monitor
is called VGA. For example, to set the external monitor resolution to 1680×1050:
xrandr --output VGA --mode 1680x1050
To turn off the laptop screen:
xrandr --output LVDS --off
I recommend to put a small script in your path that turns the laptop screen on:
xrandr --output LVDS --mode 800x480
(use the appropriate mode for your Eee)
See the xrandr man page for more advanced usage (e.g. having a large virtual screen display on both the laptop screen and an external monitor).
Finally, here's a picture of my Eee 701 with its 7 inch screen driving a 52 inch Samsung LC52M87 :-) (at 800×600 in this picture, I couldn't get it to do full HD at 1920×1080...).
