The pup probably has plenty of it's own roots by now. It probably has a single tap root which grew from the tap of the mother, so all you have to do is dig them up and snip the pups tap root, leaving it as long as possible. Don't water the
plants for several days to allow the cuts to callous over.
cactus will begin to root and will settle in
much quicker when the soil temperature is 70-75 degrees, so that should be a consideration when you are deciding when you should divide it.
Pups which attach to the ribs of the mother can usually just be plucked off fairly effortlessly and then rooted.
Dividing
cactus is very easy to do. Don't be scaredy cat!