Hello, were you just burning wood in the fireplace or was there anything else in there?
How much do you think she consumed?
How much did she vommit and is she acting any differently?
I don't think you have anything to worry about at this point. She more than likely just vommited because of the initial upset to her stomach. I would just keep an eye on her and make sure she is eating and drinking normally. If she goes off of her food or starts to vommit all of her food back up you may want to seek a vets help just to make sure she has not blocked herself with any weird piece of wood etc. Otherwise I think you will be fine you may see some darker stool in the next few days and that is normal considering the ash she ate. As far as why she did it is it hard to say for sure. Eating somehting like that may be a clue to the fact that she feels as though she is missing something from her diet. There are some suppliments out there that have small amounts of ash in them also. Someone may have also thrown something or droped a crumb or something in the fireplace or near it and she went to try and eat it and got some ash in the process. It is really hard to say for sure but given the opportunity dogs will confuse us with their actions more times then none. I do feel however that you will be fine and your baby will be fine with everything. Just keep an eye on her for the next few days and if something just doesn't seem right to you get her to your vet. You can also try giving her a bland diet for the next few days just incase the ash makes her stomach upset. You can boil some chicken or ground beef and rice to help things more though and settle her stomach if it becomes upset. I hope this helped but if you need anything else be sure to let me know.