Ivermectin is commonly used as a heartworm preventative in dogs. Even in some herding breeds that may be sensitive to Ivermectin it takes a higher dose then would ever normally be given to cause a problem.
I'm sorry to outright disagree with you but this is incorrect information.
Even trace residues have killed dogs who are sensitive, and some of them were previously regularly wormed etc with it without having reactions to it; there is one documented incident of a dog developing the gene mutation that causes extreme intolerance to Ivermectin despite not previously possessing that mutation (she'd been tested at a vet as she came from a family known to be sensitive, and previously, she wasn't sensitive).
I seriously doubt there would be enough Ivermectin residue in the chickens poop to affect a dog, even one that was sensitive.
Dogs have come to harm from residues in feces, doubts notwithstanding. If you didn't read the thread I linked to, it'd be probably worth the while.
We keep herding breeds on the ranch so I have definitely been over all of this with our vet.
On this note it's always important to get a second opinion. Vets and doctors are not infallible and they fairly regularly lack complete knowledge on a given topic, which not infrequently causes deaths.
Vets etc also subscribe to different beliefs than one another and will argue with their colleagues about the facts of a matter, while telling their customers it's fact beyond a shadow of a doubt. Far too many people trust one single vet or doctor without question, but that's not a sound basis, unfortunately.
Ivermectin is however a very ineffective dewormer for chickens. You would be much better off using Valbazen or liquid Safeguard for goats, that would also remove any concern of the dog lapping up an residue in the poop.
It does appear ineffective for almost all American chooks but does work for isolated groups and in some other countries. Depends on the prevailing rate of overusage and resistant worm population.
Best wishes.