Do you make your own dog food or purchase bagged food in the store? Either way, an idea would be to use puppy or performance good as they're both higher in caloric value, nutritional content and are easier to digest than regular dog food.
The actual amount of food you feed really depends on your dog. How has she handled the shorter hikes? Have you noticed an increase or decrease in appetite during and directly after the hikes? How she responds to the shorter hikes will help indicate how she'll handle the longer, overnight trip.
You may want to try out the dog food calculator here: http://www.dogfoodadvisor.com/dog-feeding-tips/dog-food-calculator/
It's a nice way to compare her current calorie needs to the calculator results then, compare them to the results for increased activity. Depending on how active your dog is now versus how much she'll do on the trail her caloric needs may be just slightly elevated to doubled, which is another good reason to monitor her on the shorter hikes.
And, in relation to your question dogs have a carnivorous bias while having an omnivorous ability, meaning they are designed to eat meat but can handle me plant material. Feeding a grain-free diet will help limit the amount of food you will need to carry for her because grain-free food has a greater protein content, is more calorie dense and more easily digestible.
While you didn't actually ask this dogs are susceptible to giardia protozoa, like humans, so you will need to filter or treat her water too.