If it's purchased as a round trip on a single itinerary then you're definitely protected. If purchased as separate itineraries then the official answer is you're not protected but in practice you can probably find an agent friendly enough to rebook you.

The problem in either scenario is that you could land with technically enough time to make the turnaround, but not enough time to get the cats from outside the secure area and make it back to catch your flight. In this case it's not Deltas fault you missed your flight. While you could probably find someone nice enough to rebook you, you don't have as strong a case if they try to charge you. You could also run into problems with rebooking while flying with a pet as I believe they restrict the number of animals they'll allow on a flight and your rebooked flight could already have animals on it.

I'd just go with a safer turnaround time and go get yourself a meal in ATL.