September 2015 - last edited May 2016
Veteran status in Battlefield games is calculated by taking the total number of Battlefield games played under your Origin account and subtracting 1 (i.e. if you played Bad Company2 and Battlefield 3 your veteran status would be 2-1=1, if you have only played Battlefield 3 it is 1-1=0 or no veteran status) because you are only a Battlefield game veteran after playing more than one game - veteran status is not dependent on rank in Battlefield 3; only the number of Battlefield games that you've played in the Battlefield series.
The easiest way to automatically update your veteran status is to play the Battlefield games while logged in with your Origin account - this will automatically update your status.
Since the M1911 is the veteran weapon for Battlefield 3 you must have a Battlefield veteran status of 1 or greater to access it. That means that you've played BF3 and at least one other Battlefield game while logged into your Origin account. If BF3 is your first Battlefield game you can get veteran status inexpensively by purchasing a copy of Battlefield Bad Company 2 and playing it while logged in with your Origin account or on the console account that you've already linked with your Origin account.
The EA Gun Club has been officially closed down. That means that the only way to obtain the M1911 in Battlefield 3 is to have a veteran status of 1 or higher. Please see above for further explanation on the veteran program.