I hope your dog is doing ok. Zinc is a dangerous metal that can cause not only severe irritation to the gastrointestinal tract if swallowed, but also a condition called hemolytic anemia. This condition occurs when the body starts destroying its own red blood cells in response to a toxin (only certain toxins, Zinc being one). The end result is anemia (low red blood cell count), which makes it hard for the tissues of the body (brain, kidneys, other organs) to get oxygen since the red blood cells carry oxygen to the tissues. Signs of anemia include weakness, lethargy, decreased appetite, and pale gums. In severe cases we can see kidney and liver dysfunction due to lack of perfusion.
Since your dog recently ingested the battery, it's worth trying to induce vomiting. This can be done at home (if you want to do this, write me back and we can discuss). Induction of vomiting should NOT be done if gastrointestinal signs are present such as vomiting or diarrhea, as this can indicate that the battery has burst open and we don't want to spread the chemical further.
It also would be appropriate at this time to seek veterinary care for your pup. They will take an x-ray and determine where the battery is within the body. If it's still in the stomach, they may induce vomiting if they feel comfortable given her overall condition. If it's progressed past the stomach they may recommend surgery to remove the battery. Either way they will likely perform blood tests to establish her current red blood cell count and liver and kidney values.
I don't think this a case where it would be appropriate to watch and wait, as we want to remove the toxin from her body as soon as possible to avoid severe illness.
I hope this helps! Please let me know if you need any clarifications. I wish you both the best.