first aid, beyond what you’d carry for yourself:
a roll of vet wrap and a roll of tape – or boots, as the most likely issue will be with her paw pads, if she’s not used to hiking this far. A small bottle of hydrogen peroxide to induce vomiting if she eats something (e.g., mushrooms or unidentified plants), or for cleaning. Ask your vet for a dose of rimadyl or other appropriate pain killer.
[edit: check your local shelter, parks department, or REI for pet first aid classes. Also, carry a list of emergency vets (phone and address) local to the area you’re visiting in your car – you might not have cell reception to google them]
Good luck, and have fun!