There are a lot of people who run with their dogs. You must only be mindful that they want to please you, and WILL overexert themselves to do so. Make sure you have water and a bit of nutrical for him/her. It may interrupt your "stride", but will need to be done for safety. It also makes a difference if you have a 5 pounder, or a more "substantial" furbaby - bigger ones being more, um, suitable.
As far as a means to carry the pup, yes: there are carriers like backwards back-packs that you wear across your chest, just like a baby.
You're lucky to have a pup that matches your hobbies. Mine match mine, too: they like to play fetch while I sit on the couch and toss balls down the hallway for them
Just be mindful of the pup's "training", not to overtax his tiny system. I don't think he'll ever be able to do the Boston Marathon with you (except in the pouch, maybe!), but shorter runs should be OK.