Here are some tips from this video for spinning pet hair on your spinning wheel:

You may want to blend your pet hair with other fibers you can use hand cards for this
You can gather most of the fiber from the hind quarters most of the fur is an undercoat. Shorter dog hair like a lab, would not be spin-able just because there's no soft undercoat, it's just too course.
You may have to gather hair from multiple pets or multiple grooming.
While you want a good bit of twist to hold the fiber together don’t go too fast because you make get too much momentum behind these delicate fibers. A smooth quick rotation with slower feet like seen on this SpinOlution Monarch is ideal.
Will spin similar to Angora or Alpaca.