@Andrea1160 hello fellow pet-friendly host! Your rules say you allow well-behaved dogs and that the guest needs to clean up after them. There's no mention of having to contact you about it. If you want them to, I would definitely add that to your listing rules, along with the note about not leaving them unattended. I think it's the courteous thing to do, but as a host who allows guests to bring pets also, I find a lot of people don't mention it prior to arrival. As a guest I always message in advance to ensure my dogs are welcome before booking.
In the case of this guest, they've said they won't do it again: I would leave it at that unless it's reported again (unless they seem like bad guests in other ways and you're considering getting rid of them?).
Maybe also start specifically asking people before their stay if they're bringing a pet, then reminding them of the rules if they say yes.
The fee thing is up to you. I've been hosting for 3.5 years and have never charged: I just build it into the pricing because the majority of my guests do bring at least one dog. For me, charging a seperate fee just adds to the complications, and I think it also makes it more likely that people will try and get away with bringing a pet without paying. However, lots of other hosts do successfully charge seperately, so it's a personal preference.
In my years of hosting pets, I've almost never had a bad experience. I love hosting dogs, and I think it really does increase your bookability. I would just be more specific about your expectations in your rules.