breathing, panting, high heart rate while sleeping...
Hi
Puppies do tend to breath erratically when they're sleeping. They may pant, shiver, whine etc. and it's most likely just that they're dreaming.
It may be worse when a puppy is scared or anxious and if you've just brought your new puppy home then that could be a factor here.
As long as your pup doesn't display any signs of breathing difficulties, seizures and so on when awake, it's probably not anything to worry about. However, I would advise having him/her checked out by your veterinarian to make sure all is well.
As you're a new puppy parent, you may find these pages helpful Bringing Home A New Puppy and New Puppy Care
Hope this helps, best of luck.