How to find out what year model my Mac Mini

I got a "message" dialog on screen from Apple telling me OSX Mavericks is available for free. The system requirements say my Mac Mini needs to be an "early 2009 or newer" model. I got my Mini at the Apple store in town in 2010, but for all I remember now (not much) it could have been an older model than 2009. How do I determine if my Mac Mini is a 2009 or later model? (The "About this Mac" info doesn't have anything I can interpret that indicates what year my Mini was manufactured.)

I assume Apple "has my number" and this upgrade announcement wouldn't show up on its own without software update determining (outside my view/knowledge) that my Mini is "new" enough, but is there ANY info in that "About" screen that identifies the model by year? Hidden in one of the strings of numbers and letters, maybe?

Is it concerning that Software Update didn't list Mavericks as available for my Mac? It does newly list the migration assistant upgrade to help with Snow Leopard (installed) to Mavericks. But is it worth dl-ing for hours tonight if I only have 2 gb of ram and don't know for sure if my 'puter is new enough?

*I was under the impression, since I bought this machine, that OSX 10.6.8 was the "highest" operating system the Mini could support. Has that changed?