There are possible reasons for these signs, which we can go through, but I would recommend a visit to the vet as your dog is quite young to be having this type of problem.
Given that you are in a warm and humid climate, then it is worth considering heartworm disease as a possiblity, and even if it is not present, it is an important disease to prevent in that sort of climate. Dogs can be infected via mosquito bites, and the tiny worms can live in the pulmonary artery (the blood vessel that runs between the heart and the lungs). Symptoms can be variable, but coughing especially after exercise is one of them. It is important to diagnose this disease and get it treated if it does exist, as dogs can get very poorly. Diagnosis can be made based on a blood test. More information is enclosed here:
Another parasite that is worht considering is lungworm. I know that in the US this is very much a geographical disease but is present - your vet will be able to tell you more. It is certainly becoming more prevalent here in the uk and appears to be pften associated with dogs that play with or eat slugs and snails. Usually, nasty infections are present n dogs younger than yours, but again it is worth bearing in mind and preventing if possible.
More info here:
I would also consider other forms of heart disease too. Even a very subtle heart murmur can cause these signs in a big dog, amd again, the sooner these things are detected and treatment started the better.
I definitely think that a vet exam and poss investigation with blood tests and a chest xray os warranted here. Best to play safe.
I hope this helps,