I'd ask your vet when it's ok to start running. As a general rule of thumb, I've always heard you should wait until they are at least 1 year old.
I started running with my very energetic Jack Russell about 6 months ago. She wears her usual harness but I bought one of those hands-free leashes that go around your waist with the bungee cord in it (https://www.amazon.com/gp/product/B07KPSX4SZ/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1). That works very well for us.

Before we started I downloaded one of those couch-to-5k apps. I got this one (https://www.active.com/mobile/couch-to-5k-app) but there are plenty out there. That way I was confident we were not overdoing it. It starts you out very slowly and lets you (and your pup) build stamina. We're now running 5k almost every morning and it is her new favorite thing in the world.
A side note: I actually have 2 Jacks. They are both super energetic and I originally planned on running with both of them. The boy made it very clear, very quickly that while he loves to run and play with other dogs all day long, loves to chase after a ball for hours and turns into Usain Bolt if he sees a squirrel, he absolutely HATES to go for a run with us. So he now stays on the couch while the girl and I run. Listen to your dog. He/She will let you know if going for a run is something they want to do :)