No, it is not currently possible to run IE11, and thus the F12 developer tools bundled with it, on Windows 8.
IE has only been announced for Windows 8.1 and Windows 7. The preview is currently only available bundled with Windows 8.1 (Edit: and now for Windows 7). As windows 8.1 will be a free upgrade, it may be than IE11 will never come out for Windows 8, but that is just speculation.