ArmySon:
I am left eyed dominant, and right handed. I also had lasik one month ago. It doesn't "correct" the dominance.
Also, I must second 2shots about choosing your surgeon wisely. Definitely shop around. And do your homework. Your eyes are not something you want to screw up. Please don't be fooled by budget lasik either. Most of the horror stories I've located were from this. A reputable surgeon is a must. Lasik isn't for everyone, and isn't a cure-all. But when it works, it really works. A friend of mine went from 20/1600 (no, I am not making this up) to about 20/30. Not perfect, but pretty close. I went from 20/400 to 20/20.
Good luck on it.