I think what makes this site so great is the very thing that is causing this "problem". That is the ease of asking questions for a new user. You can't take that away like so many have previously said. And I think the bad questions just goes with the territory. Which is why the voting system is so important.
What might be an appealing alternative is an elite section of Stackoverflow, where higher level, more difficult questions are the focus. There would be rep requirements to ask or answer on these questions.
Another option, would be to allow users to set filters. Then their account won't see questions of new or low-level accounts. I myself, don't have issue with "noob" questions and am happy to help. But avoiding obvious duplicates would be nice.
It would probably be easy enough to analyze for question duplicates using text similarity algorithms (http://php.net/manual/en/function.similar-text.php)