63 years as a dog companion here: Airedales to Newfies, Mutts to Rotties to Pits. Being a long-term rural-boy, albeit in the Northeast, don't believe I've ever picked up a poop, though I've shared my "sit-downs" over a lifetime.
It is from that perspective - noting the unwavering loyalty, unconditional love and acceptance across years and breeds, that I note NO dog (nor pig nor goat nor tiny pony) has a need to fly except in the most extreme and rare circumstance; and, frankly, I doubt even THEN.
@Boris Badenov got it right. "Drive, take a boat" (walk or ride a bike), or simply stay at home. The wedding/graduation/even funeral will go on without one's presence, and without the associated stress on an animal, be they legitimate "support" or not. I've missed all of those events over the years personally, for varied reasons. Life goes on, in its' fullness.
Actually gonna' say a dog's "snappy" reaction to the stressful unfamiliarity of strange crowds, a tiny ERJ or CRJ, is the fault of a self-centered owner who can't see beyond the end of their own nose ... "richards," one and all, for putting a faithful companion into an overwhelming situation.