My thoughts on dogs at wheeling events:
I love dogs, and currently have one and have had several over the years. That said, I wouldn't bring my dog wheeling for several reasons. Having your dog out there requires that you pay attention to it, and I've wheeled with too many folks who ignore that rule to feel good about dogs on the trail.
I haven't seen one die yet, but have seen several close calls where someone's dog almost gets run over on the trail. This would be a terrible thing for the dog, the owner, and the person who accidentally runs it over. Grief all around, easily avoided by leaving your dog at home or in camp.
Dogs that can't get enough attention and are constantly jumping on you, getting underfoot, or tripping you by bringing you a stick every ten seconds. Once again, completely avoidable by leaving your dog at home.
Dogs raiding food at camp or excessivelt begging. I've lost packs of hot dogs, blocks of cheese, and bags of chips to dogs foraging around camp and even opening a cooler and rooting through it. Not at all happy when the food you planned, bought and brought out gets eaten by someone's dog.
Dogs constantly barking or whining. Nothing disrupts the sanctity of camp or the trail like loud dogs that won't shut up. If the dog is constantly barking or whining, it's a sign he's not happy, and probably should have been left at home.
Most of these are simply owner control issues, and unfortunately some owners love the thought of having their dog in camp or on the trail with them, but do little to nothing to control the dog. I've also had a few dogs on the trail or in camp that were very well behaved and the owner paid attention to them, so I'm not completely biased on the subject.
Bottom line: If you plan on bringing a dog out wheeling, treat it like you would your kid. Pay attention, discipline it as necessary, and do everything possible to ensure it doesn't hurt itself or others or ruin someone else's trip.
None of the above is a slam at you, you may be the greatest dog owner in history, and if none of the above applies to you, then please disregard and accept my apologies. IMO, dogs and wheeling are generally not a good mix. But if you have it all worked out and it's never been a problem, then it's totally your call.
All that said, dogs and wheeling/camping are generally a bad idea, but it's up to each owner to decide if they want to or can do the work necessary to make it enjoyable for themselves, the dog, and other folks on the trip.