I think the biggest point of contention really is firearms in general. If you are honest and clear in the "so...what do you like to do in your spare time?" phase of getting to know each other, she's going to have processed that you like guns, you own guns, you shoot a lot, guns will be part of your life -- and hers, too, if things continue.
If she's comfortable with that and you get to a second date, third, fourth, etc., then the idea that you would have one with you while you're out and about won't seem more than just a little bit stranger.
But you've got to establish yourself first as someone she likes, admires, trusts, and wants to spend time around before you start into the more socially unusual aspects of your life, like the fact that you have a loaded firearm with you at a romantic dinner.
There's no reason to continue to waste your time and hers if she's never going to be comfortable with your guns and your shooting hobbies. BUT, once you've crossed that bridge, and you know that she accepts and understands guns as useful tools with legitimate purposes, letting her know that you keep one on-hand for defense, always, is a small step.