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.
Other small kits are wearable and built into everyday carry survival bracelets or belts. Most often these are paracord bracelets with tools woven inside. Several tools such as firestarter, buckles, whistles and compass are on the exterior of the gear and smaller tools are woven inside the jewelry or belt and only accessible by taking the bracelet apart.