Great tips summarized in this thread! It would be hard to add much more that is of importance.
I've got two dogs that hike/trail run with me regularly. If I am the guy with two dogs that was spotted on Langley, it was me that had AMS and me who could barely move forward, not the dogs. Lesson learned regarding pacing myself.
I have a 90 pound golden-yellow lab and a 40 pound Kelpie (sort of like an all black border collie). The keys for the dogs are keeping them supplied with water/snow sources, avoiding hot, sunny hikes, keeping them in shade to cool off if water/snow is sparse, and preparing them by getting them out on walks/runs regularly to keep them fit and to keep their paws toughened/callussed. Keeping dogs on dirt as much as possible is helpful to dogs' paws, not to mention to the joints of the 230 lb. owner (lots of rock/pavement is hard on most of us).
My dogs have done tons of long hikes/runs/summits, some at high elevations and in rocky terrain. I have had to carry both dogs when I slacked on paw toughening preparation (not fun when their combined weight is 130 lbs.) Aside--helicopter out for dogs sounds crazy and irresponsible to me (BE PREPARED). I have run into a hiker on the Lost Coast Trail (N. CA) who barely made it with a struggling Saint Bernard (paw issues). Another Side note-My lab is also capable of maintaining high speeds in front of a bicylce as long as rest periods are permitted.
As mentioned, I did not pace myself well for the altitude of Langley, but the dogs were mostly fine. A brief period of AMS/dehydration was noticed in the dogs when almost at the summit (brief vomiting). I will not take them up Whitney becsuse I prefer to avoid other people and other dogs as much as possible when I take the dogs hiking with me. Having said that, if you follow the tips in this thread and have the right dog, the possibilities are almost endless.
