Summarize this article:

This could harm her or dye her mouth. Watch her for signs of licking and distract her until the habit is formed. Her skin is just as sensitive as ours. Watch for biting, scratching, redness, or swelling.  If this occurs, take her to the vet immediately. Just like dyeing human hair, an animal’s dyed fur will fade over time. If you want her to keep her vibrant looks, apply the dye as needed. If she suddenly stops eating, become aggressive, bites or licks her fur, consider removing the dye or taking her to the vet.

Summary:
Avoid letting your pet lick the dye. Watch for an allergic reaction. Acknowledge color fading. Observe behavioral changes in your pet.