Hello, I am sorry to hear about Oakley getting into things that she should not have.
The good news is that sounds as if she ingested very little, if any at all, and the ingredients in this product at the levels they are present in are not very toxic. It appears the active ingredients are menthol and zinc.
Menthol can be a gastrointestinal irritant so she may have some nausea and diarrhea but because she is a big dog and she ate very little chances are you won't see any effect at all.
Zinc can be toxic in higher levels in dogs but this product is only 1% zinc, and she ingested less than 1/2 an ounce. A lethal dose of zinc is 100mg per kilogram (2.2 pounds) of body weight. If she is 50 pounds she would need to eat over 2,200mg of pure zinc. An ounce (30 grams or 30,000mg) containing 1% would contain 0.9 grams or 900mg of zinc, far less than a lethal or toxic amount and realistically she ate far less then that. Signs of zinc toxicity include vomiting, diarrhea, lethargy, red blood cell destruction leading to jaundice (yellow color to skin, mucous membranes and whites of the eye), heart rhythm abnormalities and seizures. I highly doubt you will see any of this. If you do a blood test can be taken to assess zinc levels and treatment can be started.
My concern would be if she inhaled a lot of the powder that could be very irritating to her lungs and bronchi. You do need to watch her for signs of a cough, increased respiratory effort and exercise intolerance over the next several days.
At home you can give either:
1) Pepcid ac (famotidine) at one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at one 10mg tablet per 20 to 40 10 pounds of body weight every 24 hours
These are acid reducers and should help settle her stomach as well as change her stomach pH so she is less likely to absorb any zinc she took in. These won't hurt her if she doesn't need them but may help keep her well.
At this point other then giving acid reducers I would watch her and see what happens.
Best of luck with your pup, please let me know if you have any further questions.