One final point on probability. It may not be immediately obvious, but having damage from two d6 weapons is better than having a single 1d12 weapon. The more dice for the same maximum outcome, the better!
Results with several lower-value dice are more consistent than one higher-value die, and using more dice raises the minimum outcome (using the scenario proposed in the question; 2d6 will roll at least 2, rather than 1d12 which will roll at least 1). And if you want more maths; the average for a roll of 1d12 is 6.5, whereas the average for a roll of 2d6 is 7.
Maths aside, it’s always best to try and build a character you’re going to have fun with, but you’re certainly not hamstringing yourself with two-weapon fighting, in the right mix, it can be very potent!