My dog uses a
ruffwear approach pack to carry all his food, water, treats, and poop bags. They're extremely well made packs. Find one that fits perfectly. My dog is small, and we tried some of the bigger packs from ruffwear, but they didn't fit my dog well, so we went down to the approach pack. I think it'd be enough to do a 4-5 day trip. Any more, and I'd end up carrying some of his food.
We bring some of
these booties for him when we go to the desert (to prevent tumbleweeds and cacti from entering his pads), it might not be a bad idea to get some. They're cheap and work so much better than the booties they sell at pet stores. I'm convinced that 99% of the products at pet stores are marketed to the dog's owners, not the dogs themselves. Vibram-soled ruffwear boots are appealing to dog owners, not to the dogs. The boots I linked to above are awesome.
Just like a human, your best bet is to practice on some smaller trips where the consequences are lower. Practice river crossings, practice estimating her food, etc. My dog eats about 3x the amount of food while camping than when he's at home. Figure out her food/water needs, and spend a few nights camping outside with her.
Other precautions are with wild animals. Dogs can often irritate a bear or moose, and then run back to their owners. The bear or moose will chase the dog back to their owners and attack the owners too. Don't forget that the dog's food will attract other animals as well, so treat it like the rest of your food.
Dogs are the best, and they can do really well backpacking. They can also be a total nuisance to others, so make sure your dog is extremely obedient, friendly to other dogs it may encounter, and friendly to strangers. My dog doesn't sleep at night, he stays alert watching for danger. That took some getting used to. He is my best buddy, and comes on 95% of my camping trips.