Hopefully, you and your pet will NEVER have a medical emergency but it is always good to be prepared. Whether the emergency is big or small, a pet first aid kit is important to have available to make your pet comfortable until you can obtain veterinary care.
To put together an integrative pet first aid kit, here are the supplies we recommend:
(None of these suggestions are intended to replace professional vet care. In the event of an emergency, get your animal companion to a vet ASAP!)

Essentials:
Bach Rescue Remedy** - For stressful situations, pain, fear. This provides immediate calming effects. Most easily administered in liquid form. This can be dropped directly in the mouth or applied to the skin of pet's nose, ears, lips or paw pads.

Calendula Spray - or a spray product containing calendula and aloe. This is excellent for minor cuts, hot spots, insect bites, and skin irritations.

Hypericum - This is a homeopathic remedy that helps slow bleeding and reduces pain from nerve damage. Available at Amazon and most natural food stores. It works by sublingual absorption so just get a couple of pills into your pet's mouth.

Disposable gloves
Tweezers
Gauze pads
Adhesive tape
Scissors
Rolled bandages
Blanket
Peroxide or iodine
Veterinary contact info (including 24 hour emergency clinics)

Also recommended (additional homeopathic remedies):
Arnica - for trauma or injury. Especially effective if administered immediately for strains, sprains and pulled muscles.
Apis - for swelling or inflammation. Useful for bites and stings.
Nux Vomica - for digestive disturbances. Helpful with vomiting and diarrhea especially from eating inappropriate foods (or plants or garbage...)

An added bonus is that all of these products can be used for human emergencies too!