How to get cable staples to stick in the wall
Nail in clips just will not hold in drywall.  Even over studs, the nails are typically too short to get good penetration.  Nail clips and stapes can still work (barely) in drywall if they are used up high where they will not be touched.

I would instead recommend and adhesive clip option.



The Command Clips linked also have the advantage of coming off the wall cleanly if you ever need them to.

Another good option is adhesive wire mold that covers the entire length of the cord.  It's a little more expensive, but with no exposed wire, it becomes very puppy-proof.