It is certainly better to have someone to help you restrain the dog while doing quill removal, but I have done it alone several times. Any dog of mine learns early to let me do "procedures" on them -- trimming nails, cleaning teeth, etc. They don't like cooperating with quill removal but all of my dogs have let me do it.
Probably the biggest reason it is a good idea to let a vet do it is that it is easy to miss a quill after 30 minutes of wrestling with the dog, and that can be the one that kills it.
But for me often "taking them to a vet" is simply not an option, nor is it necessary. For me quills screw up an hour of two, they don't cause me to punch out of the entire hunt. You dog or situation may differ, however.
