Are you saying that a host has not responded to your question about a property? If you have not booked a property yet, you can continue to inquire at many properties.
-If the property has instant book on, carefully read their rules and see if they accept pets, or inquire in advance if you are not sure.
-otherwise, simply inquire about whether they would accept your dog. When someone approves your reservation request (and dog), you can accept it and book the place.
If you ask multiple people, and multiple people pre-approve your booking, just book one place. That way you are only charged for one place.