I agree with the others I eat over easy eggs a lot so I would say they are fine!
I craved them too! Around the same time too, maybe at 11 weeks you need more protein? Yea I ate them. It's just a precaution to avoid food poisoning. But yea they are fine to eat :)
I eat them all the time with bacon and toast. No harm done
I eat over easy eggs all the time in both my pregnancies and haven't had any issues.