Correct, but I was connecting to an international flight (hence the urgency--the certificate had already been checked, but of course would be checked independently at the border, and, since I wasn't going to subject my anxious dog to whatever godawful quarantine-and-titer-testing process there is for animals without papers, there was no point in getting on the first flight until I had a copy).

I hope you and your Bichon had happy travels together!