the dogs head? his nose? There's only one place that you can "push" a quill "through" and that would be the lip..and then you have both an entrance and an exit hole to deal with......
Porcupine quills are hollow and will crush when you grab them with either forceps or a pair of needle nose pliers and you definately want to be very careful not to break them off at the skin and leave them in but I can't imagine "pushing them through" anypart of a dog....be like removing a fish hook from a body part by shoving it the rest of the way through the part of the body where it is stuck.....I'll pass both on having it done and on doing it....
My first Lab was a Porcupine hater and never missed the opportunity to jump on one and never seemed to figure out the cause and effect of it.....funny how some will learn after the first time and others never do...interestingly he was exactly the opposite on skunks...sprayed lightly once he forever after that gave them a wide berth..
This is him during a "de-quilling" on a Quail hunt. probably 100 in the face nose and lips and another 100 or so inside the mouth which werre the scary ones..
By this point I was exhausted and he had just about chewed my thumb off which I had in his mouth to keep him from shoving the ones inside his mouth in deeper.....
Interestingly the ones inside the mouth were the easiest to remove since the skin didn't stretch out like the lips and jowels will do.....
This was many years ago and I'm certain that if that had been me with the quills in him I'd have shot anyone that tried to remove even one, much less "push it through" wherever it was stuck......
I figured we were done after this one but Thud just ate some snow, peed on the bloody spot in the snow, and started hunting again......
If you live in Porcupine country never go anywhere without a good pairs of needle nose pliers or forceps.....the quicker you remove them the better....
Steve