This is very common, and should pose no problem at all. I am also cross-dominant, and it has not affected my ability to hit a target when and where I want. I have been training to draw a bead with my right (non-dominant) eye though, just so I don't have to push so far over with my right arm to aim with the left eye. Right now, I can easily and quickly get a good sight picture with either eye, though I'm sure someone will reccomend that I pick an eye and stick with it.
In the end, there's nothing wrong with being/shooting cross-dominant, so just go with what works for you!
Edit to add...
Trying to shoot a long gun cross-dominantly, however, can have some rather painful consequences:quirky