I have hiked with my dog on Whitney. We've been up to Trail Camp, though not as far as Trail Crest. With some care and preparation, this can be a safe and enjoyable way to hike, for dog and owner alike, without negative impacts on the surrounding environment.
1. With respect to paws, you have to condition your dog to hike properly. I hiked a lot of East Bay Hills before trying the Sierras. We had a few mishaps (once, I did run her paws raw), that I learned how to address and avoid. Before trying Whitney, we did a number of long day hikes, including Mt. Tallac and Mt. Tamalpais, as well as a lot of hikes on Mission Peak in Fremont, CA.
2. On altitude, I have read the dogs can get altitude sickness (and have read trip reports about the bizarre ways in which that can manifest, including uncontrollable barking and erratic behavior). Before taking my dog up Whitney, I spent a lot of time with her over several weeks in the Tioga Pass area. When we did our Whitney trip, I built in a lot of acclimatization for both of us. We spent 2 nights at Tioga Pass, plus a night at Outlook Camp, before going up to Trail Camp.
3. On Whitney, because of the rocks, my dog wore booties (see second picture below). We turned around at Trail Camp, rather than go for Trail Crest, because even with the booties, I was concerned about the rock issues. Though she did the entire Tallac hike (14 miles in one day) without booties, so I was probably being overcautious. I also carry duct tape (the 11th wildnerness essential), which in a pinch, can be used to deal with paw issues.
4. Despite all this preparation, I make sure to have a pack that, if necessary, could be used to carry her down in. I don't think you can assume that a helicopter will come for a dog.
5. Dogs are great pack animals. They can carry out their own poo, and they don't mind a little extra. My dog carries out her own wherever we go ... dog poo is not good for wild animals....
6. Depending where we are, I may only allow my dog to drink filtered water (e.g., if there are livestock around, or if it doesn't appear that the water is pristine). Dogs can get parasites. However, I am a little less scrupulous about the water that she drinks than I am about my own; dogs do have strong stomachs, and there is the fact that a dog will be a dog ... even though I keep my dog on leash at all times while hiking, it is hard to be attentive to every single movement ... if we are doing a stream crossing, and she's thirsty, she may get a sip in before I can evaluate and offer filtered water instead.
7. I started high altitude hiking with my dog when she was maybe 6 years old. So far, paw care has proved to be the thing I have to focus on the most.
Happy trail dog (Kennedy Meadows near Sonoro Pass)
At Trail Camp

Overheated on the Main Trail...
