By all means, take him out jogging, but be sure to pace him as he probably won't do it himself. If he has trouble keeping up, you are either going too fast or too far. Do not push him. If he is over angulated or not structurally sound, do not run him as it will be too hard on him. My dog was jogging 3 miles a day by 6 months of age, but he had been building up to that distance for some time.
Swimming is always great if you have that available and he likes water.
If you want to get him into dog sports, you should be getting him into a club now as most of them want to begin training at a very young age.
Elaine and the herd