According to the crash log, it can't find the
DVTFoundation framework that Xcode needs to run. It seems extremely curious to me that Xcode is running straight off of the Desktop. Xcode comes with an installer, which (by default) will put it and all other things inside
/Developer. You can change it to another folder, but even then Xcode is still within the "Applications" folder of the parent folder. In other words, there's no way to get Xcode off by itself on the Desktop unless you copied it there or didn't install it properly.
Xcode, like a couple other Apple apps, requires a whole bunch of supporting things to run (like this
DVTFoundation framework). You have to leave it in the place where it was installed. Moving it to another folder is a great way to make it not work (yes, I know this isn't ideal, but it is what it is).
To fix this, trash the Xcode.app on your Desktop and re-run the installer.