The first thing anyone should do with a new puppy is take it to the vet asap for a thorough check up. You can discuss these episodes with the vet to make sure it is not something more serious.
Two of my dogs have similar episodes that sound like gagging, and it happens when they get startled or over excited, although there are other causes. It is a minor spasm condition, and usually stops on it's own within less than a minute. Only a vet can tell you for sure. Here are some links to info about reverse sneezing, in case it is helpful.
01 Reverse Sneezing (Pharyngeal Gag Reflex) - VeterinaryPartner.com - a VIN company! Sneezing, Reverse Sneezing (gasping in for air), and Gagging in Dogs | petMD
This thread has links to some videos that show dogs with reverse sneezing.
http://www.yorkietalk.com/forums/sic...2-weezing.html