Oh, man. Nothing but sympathy to you. Marriage is such a strange thing. And there's so much that we (or others) notice only in hindsight.
Personally, I would be way, waaaay more anxious about accidental poisoning, knives, falling down stairs or any of a million other things that can harm a child. Is she like this regarding these other kinds of concerns? But I agree with the comment about not trying to accomplish this through fear. That's probably not the right way to go.
I like the comments about getting her into shooting incrementally. You could even start with an airsoft pistol or something. I'm going check out these other sites mentioned by others 'cause my wife is sort of on board, but I'd like to see her even more comfortable with guns herself.
FWIW, with my kid (not quite 2) I carry her around, play with her, feed her, etc., all the time while I'm armed since I carry at home (yes, my wife knows). I carry my .45 in an IWB holster with a safety on ('cause I carry cocked and locked). Actually, you could even find a gun that you could carry DA first pull with a safety as well. That might help her feel better but if she doesn't know enough to appreciate how absolutely over-the-top cautious this would be it might not help after all.
You're in a pickle, my man. But whatever happens, you need to be there to protect your kid, armed or not. Just think, if you get divorced, who might she marry? And if she convinces some judge you're a 'gun nut' that might not work in your favor regarding custody.
Anyway, enjoy parenthood. It's the craziest, most rewarding, frustrating, humbling and hilarious thing you'll ever do. Well, of all the things I've done, it's my favorite thing anyway.
Best wishes and check in to let us know how it's going.