I originally thought March 2013 but even that is looking doubtful at this point so I'm going with May 2013.
I don't even expect the beta to begin until January. The alpha isn't starting until November and that will take 1.5-2 months. I doubt SE will change from alpha to beta over the Christmas period as their staff will be on holiday so definitely January for beta.
Anything less than a 4 month beta would be worrying. It takes time to go back and fix bugs and change things. You have to remember this is a whole new game and the beta will be treated as such. 4 months for an MMO beta is on the short end of the scale, it could well be 6 or more but unlikely.
Then we will have a few weeks of open beta while the game is packaged up and distributed around the world.
Then the open beta will be closed while they transition from that and prepare the servers for release, say 1-2 weeks.
So yeah, May at the earliest.
Unfortunately GTA5 is likely to be released around the same time and I've been looking forward to that more. So I am actually hoping ARR won't be released until June or July.