What to do if you accidentally double book yourself?

I got a booking request yesterday afternoon, to which I replied right away with my questions and giving more details on my schedule. The owner didn’t reply until 24 hours later. As a result, I have been talking to a client that I have already sat for about watching their dog this weekend, assuming that the other owner chose someone else. I am not sure what to do as I would rather watch the dog that I already know and am comfortable with, but I feel a sort of obligation to take this new dog (who is not good with other dogs).