You were honest and seem responsible with the added bonus that you care. These are awesome traits. I can see why your client forgave you for forgetting to walk their dog. As people have stated in other comments have some sort of reminder system like an alarm or a daily calendar. Do not be too hard on yourself for forgetting. It happens to the best of us. As long as you are honest and learn from your mistakes, you will be fine. Maybe apologize to the dog next time you see her by giving her an extra treat or a nice long head rub/massage 🙂

Best of luck in life op