There is so much conflicting advice to be had on this subject. Also on humans, too.
I've been running for 20+ years, have rheumatoid arthritis and my doc says KEEP RUNNING (I also lift weights and have no knee issues, no ITB issues, no hip issues, etc). But all you ever hear is "running is bad for you! It'll ruin your knees!"
I think sometimes we're too careful of pups, in SOME ways. I finally took my pup on a short run (about 2+ miles) after running .25, then .5, of a mile with him. He hikes WAY more than that, and I had a funeral to go to in Montana which would put him in his crate for about 5 hours. He is 8 months old today, and this was about 2 weeks ago. It didn't even faze him. Half of the run is on the sandy, dirt shoulder. The other half is on asphalt. I had to play ball with him when we were done, even.
I would for sure start slow, be prepared to stop and walk if the dog shows signs of not enjoying it or needing to, and mind the weather. I never run during the day if the temp is over 70-75 (we don't have much of that weather here, unfortunately), I will go either early in the am or after 8pm at night. I would start him/her slow, and try out some trails if you have access. I will be doing more trail running once the snow/ice is gone. Right now we can only hike.
They say running on paved surfaces is bad for people, too, but I'm in better shape than many of the people I know.