are dogs on leash allowed?

Yes just watch for alligators

I'd keep any dog on a leash and very close to you, and be prepared to run. Gators see dogs and other small animals, to include small children as prey. And they will attack. That being said, you have been warned. Enjoy the Everglades and please don't pollute. If you see trash on the ground, please do the Everglades a favor and put it in a trash can.

I never saw any restrictions about that but you'd better make sure it is on leash. Plenty of wildlife to chase there.