Compact LG dryer wiring.

So here is my dilemma.

I got a new lg compact electrical dryer. I need to upgrade from a 20amp breaker to a 30 amp. And I will also need to run 10 / 3 gauge wires.

However, I noticed that on the inside of this compact dryer there is a sticker that says 120 / 240 13a.

My question is it safe to use the existing 20 amp breaker with the existing 12 / 3 gauge wire? While I understand that code will probably strict on this I would like to know if it is possible? And what would be the side effects of running the dryer like this. Would it be OK if I run the dryer on lower settings? Would the breaker simply trip or would there be bigger problems?