You can also do it with adb:
# busybox cp /data/data/com.rovio.angrybirds/files/*.lua /sdcard
# cd /data/data/com.rovio.angrybirds/files
# ls -l
-rw-rw-rw- app_114 app_114 16668 2011-06-10 01:22 highscores.lua
-rw-rw-rw- app_114 app_114 1521 2011-06-11 11:15 settings.lua
# busybox cp /sdcard/highscores.lua .
# busybox cp /sdcard/settings.lua .
# chown app_114.app_114 *.lua
# chmod 666 *.lua
You can also complete the first level (so that highscores.lua gets created with correct permissions), and then restore using:
# cat /sdcard/highscores.lua > /data/data/com.rovio.angrybirds/files/highscores.lua
# cat /sdcard/settings.lua > /data/data/com.rovio.angrybirds/files/settings.lua
You can also use titanium-backup to back it up. Restoring with titanium might not always work, but don't worry, the .tar.gz generated with titanium contains the two required lua-files, you can just extract them from there.
Also, iirc there is some free app on the market, that can do it without root (no idea if it still works). Just don't buy the paid ones.