One Advil pill for an 18-month old shouldn't cause serious problems. You can always call poison control -- in the US the number is 1-800-222-1222. They're very helpful and they don't judge or ridicule. Great blog post on this in the related links.
I am not a vet, but I don't think that you have anything to worry about. Some vets prescribe advil for dogs with arthritis. Your dog is large enough that one pill should not adversely affect him/her.
my Chihuahua ate a penicillin pill what can I do
What if my dog ate my lunesta pill
Contact your pediatrician for advice.
Your dog will be fine, but make sure they do not hurt themselves (if the pill is meant to make humans go to sleep it might be disorienting to dogs).
Of course it is a problem if a toddler ate (ingested) baby powder! Call your doctor to see what they recommend.
My puppy accidentally ate a 25mg prednisone. What can I do ?
no
"Depiliate" (dee-PILL-ee-ate).
Zero.
Nothing (other than find a new place to keep your string). "This too shall pass."
you ate too much