Current draw and VA ratings
I think you are making a simple math error. As a first level approximation 12 VA (VA stands for Volts x Amps, referred to as Volt-amperere) = 12 watts. If the load is purely resistive then VA and watts are the same, if it has a reactive component (think capacitors and inductors) then the wattage that can be drawn is less than the VA. 

12 watts at 120 V =0.1 A not 1 A. Similarly 12 watts at 12 V = 1 A.

If you need to draw 2 A (or 24 watts) from the secondary then this transformer is not going to cut it for you.