I've never had vermin problems either but I have two barn cats that pretty much eat everything but my chickens. I even had one bring me a young rabbit. Also my chickens are pretty good at taking out vermin I've found a few dead mice in their pen. oh well I suppose it's all in one's opinion. the fear of having vermin bring bacteria in is completely logical. I say just do whatever you feel comfortable with. If you don't want her to have any chicks just keep taking the eggs out and if she continues I would suggest trying to break her from it just so she can get out in the sun with the flock. You can eat the eggs so long as their fresh it doesn't matter if they're fertilized