My wife and I took our 10 year old dog on a 34 hour cross-country in my
182. We did not have any hearing protection for her to use and I
believe that the noise caused her permanent hearing.

I've never found a product for protecting a dogs hearing. Does anyone
have a referral of a product that works well for them?

I *highly* recommend that you find a way to reduce the noise-levels for
your dog. I wish that I had not assumed that flying without hearing
protection for my dog would not cause her hearing damage.