If you plan to anchor out frequently, especially if you have a dog on board, the answer is YES. You will need a dinghy to go ashore for supplies when anchored out or to bring your pet for “shore duty.”
We didn’t anchor out much, and we didn’t bring a pet on board. We only used our dinghy a few times the entire trip. Getting our dinghy off our boat is a bit of a chore, which probably impacted our usage. We used it once while anchored out to get to shore and the rest to just explore the area we were in. We took a ride up a creek off the Hudson River, and we explored the mangrove islands to see the manatees in Florida.
If you don’t plan on anchoring out, you may not need it. One consideration, either way, is how you carry it and how easy it is to get on and off your boat. Swim platforms or transom-mounted dinghies can increase your overall length, which may be a cost/availability issue at some marinas. Dinghies that take a lot of effort to deploy, like ours, may reduce your willingness to use them. I would say that most Loopers carry a dinghy; however, we did meet a few without.