Xcode appears to be installed but xcodebuild is unusable
Did you run sudo xcode-select -switch /Applications/Xcode.app? This message: error: can't exec '/Developer/usr/bin/xcodebuild' is telling you that your system is looking for xcodebuild in `/Developer/usr/bin/' but as of Xcode 4.3 (the one that's installed from the App Store) it's located in the Xcode.app bundle which is in /Applications.

Edit

In a comment to your question you say you've run sudo xcode-select -switch /Applications/Xcode.app. Now run xcode-select -print-path and make sure it says "/Applications/Xcode.app". 

Also, you may need to download the command line tools separately. (I don't know from first-hand experience because I'm stuck on Snow Leopard for the moment so I haven't installed Xcode 4.3.)