I can't speak from direct personal experience, but I had a roommate who only had sight in one eye. He was able to drive, and it wasn't any scarier riding with him than with any other late teen / early twenty-something driver. He used a variety of techniques to determine speed and distance without depth perception -- reference objects, rate of changing size, etc. He was an engineer and had a pretty sophisticated system worked out, but he was aware of the limitations and drove cautiously.
Pilots use simulators to gain experience without risk, and there are some good driving simulators out there. The false 3D on a 2D screen might actually be a bonus in your case. I've heard good things about
$1, but it's a game and there are probably more realistic options out there.
tl;dr Best of luck, you can definitely do this.