Newbie like me? I know there's a lot here, but a lot of reading on this site and the FB page will help make things MUCH easier. (speaking as a newb myself)
Things could be very, wrong with this. Worst case scenario, they abandoned the dog on you. I've read it's happened. But let's not go there yet.
Best possible: cell coverage spotty/non existent where they were can lead to no replies. I just had a client like this, she responded once out of a 4-day stay, to tell me that much. Everything was cool tho.
Also, your client may be on the plane and not checking their app this morning. They may be sleeping. Perhaps another text saying, 'Please let me know asap when you will be picking up _. You may incur an additional ($amt) fee for late pickup.
Unfortunately, you painted yourself in a corner by never giving them a pickup time. Technically they haven't a clue that they can't just pick up Fido any hour they want day or night. Chalk it up as a lesson learned.