Before they were pets, dogs were workers. They can carry their own supplies without complaint (already making them superior to most humans right now), sniff out food and water, and search for and bring down prey. Some breeds, such as huskies, have been specifically tailored to bust their butts on the barest of rations. Dogs also have a long and storied history of offensive and defensive combat use, making them perfectly suited to attack anyone who thinks they have more of a right to that sweet, sweet snack cake stockpile than you do. Which is to say, your four-legged pal is just a few training sessions and a kickass set of armor away from leading you to your rightful place as God Of The Ragged Desert/Water People.
In addition, the kits may contain typical individual "survival kit" items, such as nylon tarps, extra clothes and coats, blankets, sleeping bags, matches or other fire starting equipment, a compass and maps, flashlights, toilet paper, soap, a pocket knife and bowie knife, a fishing kit, a portable camping stove, a power inverter, backpack, paper and pencil, a signaling mirror, whistle, cable saw, bleach, insect repellent, magnifying glass, rope and nylon cord, pulleys, and a pistol and ammunition.
To me, the best option is to store emergency food. How much? If you have none, store enough for a few days. If you have enough for a few days, get enough for a week. How much you store depends on what time frame you think you're at risk for having to be completely independent. The early settlers of the southwest liked to store enough food for a whole year and still do to this day!