Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your girl ingested your 60mg Armour thyroid pill.
Armor thyroid pills are a natural preparation derived from porcine thyroid glands, and thus aren't the same concentrated pill source of hormone like synthroid, thus they will be less of a dose. Although this pill is labeled as 60mg the amount of active thyroid hormone is about 0.06% of that. Dogs also take a higher dose of thyroid supplement per pound of body weight per day compared to people, so she will likely handle this better as well.
Even though she did get something she doesn't need a one time dose won't hurt your pup, if she is otherwise healthy with no history of heart disease, though it may make her a little hyper and elevate her heart rate. But with this small dose even that is unlikely to occur.
If you are worried and it has been less than 2 hours you can give 3% hydrogen peroxide at a dose of 1 tablespoon for a pup her size You can give this directly or mix with a little ice cream or bread chunks. Then take her outdoors and run her around to get the peroxide bubbling to stimulate vomiting.
If no vomiting repeat in 10 minutes.
But honestly this one time dose should not be a problem for your pup, and the effects won't last more than 24 hours or so.
Please let me know if you have any further questions.