Have her sign your release of liability in exchange for the payment. You shouldn't have to cover the ear infection unless it was caused by your pet.
I am an Attorney-at-Law, licensed to practice law only in the state of California. Unless we have both signed a formal retainer agreement, you are not my client, and my discussion of issues does not constitute legal advice. Opinions expressed herein are those of the author, and do not necessarily represent the opinions of those who hold other opinions.
If you're going to ask the owner of the other dog to sign something already, you could consider adding a provision confirming that the amount offered (and presumably received) represents full and final satisfaction of all claims, known or unknown. Of course, check to local counsel re: relevant statutes or considerations.