Your dog should be at least one year of age before running further than one mile at a time.
There is a sliding scale for terrain, age, and breed. They may be able to safely go further on softer surfaces. Some breeds are more prone to joint problems than others. Large breeds need to take is slow longer than small breeds. However to be on the safe side, one mile before one year is a good general rule.
"The leg bones grow from areas located near their ends. These soft areas of immature bone are called growth plates (also epiphyseal plates or the epiphysis). At about 12 to 16 months, the growth plates “close” as calcium and minerals harden the soft area. When the hardening process is complete, most growth stops and the growth plates are said to be closed. Before they close, the growth plates can be injured or fractured more easily than mature bone. An injury to the growth plate can cause the bone to stop growing or to grow incorrectly." - 1
The argument has been made, that your dog may run further than a mile when romping through the yard, or at the dog park. You'd be surprised how short those bursts of off leash play can be. More importantly, in typical off leash play, your dog isn't dragging a full grown human behind them. (That adds quite a bit of joint stress.) Most puppies are more than happy to jump on and off furniture all day too. That doesn't mean it's good for them. You shouldn't let them. The same applies for running.
I know you want to grab your little fluff ball and go for a run, but the risk or permanent injury just isn't worth it. I trained for, and completed, a marathon while waiting for my youngest to reach optimal age. Now that he is old enough we can finally get into training. Short runs, getting used to the sport, and learning his canicross related commands will occupy our time for now. We have to build up his endurance and I want him to have a little more time to mature.
Get out there and have fun with your best friend! Just make sure he is old enough first!
Never Run Alone