It will probably go through her just fine. She might hack up parts of the bird in the next day (and probably re-eat them). I believe birds carry fleas? So if it was a very recently dead bird, you might be on the lookout for tapeworms after a while. But I agree with the above posts; it will probably be just fine.
Milo, eater of squirrels (tail and all!), asks "Want fries with that, Sallie?"