Here is something I read about dogs and lady bugs...
have reliable sources, and have not been warned about them. What you are seeing is likely Japanese Lady Beetles, an invasive species that has been around for a while. They seem to come in the house in the fall and die. Under housekeeping advice, I have heard they are harmless, just sweep them up and dispose of them. Just because they don't eat your house doesn't make them entirely harmless. 
Unfortunately, if you don't beat her to them, then may eat them and upset her stomach. I doubt they are poisonous, but almost anything strange can upset a dogs digestion. You certainly don't want the mess, or her to lose the food she ate. No fun for her either. It might not hurt to talk to the vet. Of course to cover himself, he may say bring her in and it will be $50 for him to say what I said for free.
I dont know if dogs and chickens are the same but...