Problem "do shell script" on curl – Works in Terminal, but not via "do shell script"
I've found the solution. The problem is, that homebrew installed an optional newer version of curl, but the command do shell script does use the old version.

After a hint from a friend I used which curl in terminal and apple script editor and get different results:

Terminal says: /opt/local/bin/curl 
Apple Script do shell script says: /usr/bin/curl

So the solution for my problem is to force do shell sript to use the newer version via:

do shell script "/opt/local/bin/curl \"https://v.gd/create.php?format=simple&amp;url=http://www.test.de\""