This is a great idea!
You don't have to be traveling on I-10 t0 access the Fanny Bay Trail. In fact, the east end of the trail is at a parking area off of Pony Dobson Road in the Osceola National Forest. Good luck finding it, though. The rest area trailhead is much easier to locate. That trailhead is in the rest area for westbound traffic on I-10 near mile marker 318, just after exit 324 (US 90-Sanderson-Olustee) but before exit 303 (US 441-Lake City-Fargo). This rest area and its eastbound partner seem to have been put together by the United States Forestry Service; there are quite a few displays relating to the Osceola National Forest in particular and Florida National Forests in general.
Look on the walkways for silhouettes of frogs painted in yellow. These are the blazes that will lead you out of the rest area to the Fanny Bay Trail. The frogs take you north from the rest rooms, then west and north again to the boundary fence of the rest area. Here a gate leads through the fence, into the Osceola National Forest, and onto the Fanny Bay Trail. Turning right will take you about a quarter mile to the east end of the trail along Pony Dobson Road. You probably don't want to do that, so turn left and take the trail toward the swamp.
The trail itself is double track with a grassy surface that seems to receive regular mowing. The mower misses the dog fennel growing on either side of the trail, which you may need to brush aside as you pass. Frequent interpretive signs are posted along the trail. The weather prior to my visit had been wet, so there were puddles on the trail closer to the swamp.
Once in the swamp, the trail takes you onto a boardwalk winding through the trees. I found the tread slick, which is probably typical unless conditions have been exceptionally dry for Florida. Below the boardwalk, duckweed floats on the surface of the dark water. About half a mile from the rest area, the boardwalk ends in an observation deck with seats in the middle of the swamp. You can stop here and take a respite away from hurtling vehicles of steel and glass. The sounds of the highway are almost distant enough to ignore.
If you're looking for more exercise than a one-mile stroll to the swamp and back, consider turning right from the rest area trailhead. The Pony Dobson Road trailhead is only a quarter-mile away, but Pony Dobson Road itself is unpaved, an excellent surface for a walk or a run. Not having explored the road, I can't say how far it will take you, but I'm willing to bet that there's more than a few miles of natural surfaces waiting there for your feet.
Even just the walk to the swamp and back is a refreshing break from the highway, long enough to leave you alert and ready for more driving. Where possible this trail should be emulated at other highway rest areas. For example, both the eastbound and the westbound rest areas on Interstate 10 near mile-marker 194 outside of Tallahassee are adjacent to the Ochlockonee Tract of the Lake Talquin State Forest. Is anyone from the Florida Division of Forestry reading this?