I never bothered to upgrade my 2012 MacBook Air to Mountain Lion. Currently I am on Lion.
Can I upgrade straight to Mavericks, or do I need to first upgrade to Mountain Lion and then to Mavericks?
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According to the Mavericks How To Upgrade page you can update from Snow Leopard (10.6.8) Lion (10.7), or Mountain Lion(10.8) later to Mavericks (10.9) if your hardware meets the requirements, which yours does. I upgraded my 2012 MacBook Air to Mavericks about two weeks ago and the battery life is noticeably better.