I mentioned on an earlier post about two friends that kayak and use car roof racks to transport their kayaks. The one friend who goes to the Gulf coast all the time also has an inflatable kayak he bought on Amazon for about $300. You can put that in a golf cart a lot easier then pulling a trailer. Here's a link to Amazon and inflatable kayaks.
Amazon.com
I mentioned a friend kayaks at Lake Okahump State Park. That lake is located here on this map.
Google Maps
Lake Okahumka Boat Ramp
Lake Miona has been mentioned several times, it is within TV and they have a fishing pier, a small beach and many even water ski on Lake Miona. However, it's off of Rainey Trail which is a not a golf cart accessible road. I know people who live in Lakeside Landing, a community right outside TV on Rainey Trail and they will drive golf carts on that road and come into TV. Here's a map of the Lake Miona Park location.
Google Maps
Here is the Lake Minoa County Park Website.
Lake Miona Park | Sumter County, FL - Official Website
Lake Miona pier and beach, you should be aware all fresh water lakes in Florida will have alligators.
Lake Miona Boat Ramp