I'll echo what some of the others have said. If she wants a 22, she gets a 22. It's better than nothing. If she wants a Walther, she gets a Walther. (Personally, I think they're neat little guns.) If I carried a 22lr for self defense, it would be a revolver, easier to clear, but to each her own.
I'd like to add:
She ought to learn how to clear malfunctions, as with any semi-auto.
The 22lr is an advantage in a way, because she can get LOTS of practice, really cheap. If I carried a 22 rimfire for self defense, it would probably be a long rifle rather than magnum for that reason. And if she shoots a lot, she may be interesting in upgrading in the future.
Congratulations on having a wife who's willing to take the responsibility of carrying, along with joining you in a rewarding hobby!