I know you are saying you arent probably going to do it, but one other factor with a trailer is the wide track, and specifically with a narrow road, and or big potholes to avoid, and or a roadside dropoff mixed in with potholes or rough stuff in general.
In Honduras last year, we followed the route taken by another tourer, who was using a folding Bike Friday bike, towing the trailer of the purpose designed suitcase for the bike. A particular section one day was really really rough, narrow, road shoulder dropping off a lot, and I couldnt imagine him riding that with a trailer, especially with the traffic there was when we were there, lots of rock quarry trucks in both directions, difficult with a regular bike, but easy for me to just pull off the road if need be, and to avoid holes etc. It would have been a real bear for that guy pulling the trailer, simply from the wide track and two other tires to go into or sink into depressions etc--and he had just stuff in his trailer being bounced around, not a loved pet.
I dont know the west coast area, but around here there are a number of bike trail systems which would certainly be more relaxing for doing a trip with a trailer, so I guess that could be a possibility , but again, I dont know the details of what is out there, how long they are and if they would be interesting to go on.
Yes, when pulling my heavily laden trailer on old unused logging roads it was a big frustration trying to fit all 3 wheel tracks
around the big holes and boulders for sure. I was sitting on the fence when I started this thread, hoping to hear from others
that had toured with a big dog and done so with success which would encourage me to give it a try. After reading sensible
comments from some, and especially you, I can see it's just too much of an ordeal considering the distance and varied terrain
having to ride through. Thanks!