I have about 60 plants (10 in pots on the deck) and 50 in the ground. My dog likes to come out and watch me work on the hops. He never has expressed any interest in the plants.
Another thing, as you are growing your hops, you will want to strip off the bottom two feet or so of leaves and such. this helps reduce the incidence of mildew and promotes air circulation around the plants, as well as putting the hops out of the dog's reach.
Spent hops are quite a different story, when I clean out my brew kettle, I always put the spent hops in a 5 Gal bucket with a tight lid. If you dedicate a bucket for this purpose, drill a bunch of holes in the bottom and let the bucket sit in the sink until they are drained--easier to handle that way.
Good luck with your hops