So I found the problem (it is really stupid). I decided to start Qt Creator from the command line. By doing so, I saw error messages from clang which complained about unknown/wrong arguments and this helped me to find the problem. It is IMHO kind of bad that you never see those in the GUI...
So to make C++11 work correctly, I had to go to settings->Build & Run -> Compilers and make a copy of clang and add "-std=c++11 -stdlib=libc++" to the codegen flags. I made a stupid typo there and wrote "-std=c++11 -stdlib=c++" instead. Since Qt Creator still found all header from libc++ and had c++11 activated, I never bothered to double check this. But changing this flag to the correct one did the trick.
EDIT: Just want to add: I found it extremely strange, that Qt Creator was able to find ALL include files (I use several third party libraries at several different locations - no problem there) EXCEPT for those in /usr/include if you screw up these compiler flags.