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Looks like a cholla maybe. Cylindropuntia species? I have not seen one this small, presumably a seedling. Those plants are almost always propagated from cuttings, not from seed.
That is big enough to extract, I think. You need to be slow and careful when you do it, so as to preserve as much of the root system as possible. Hopefully the soil is not too dense under there. Make the move when the soil is nearly dry, but not bone dry and rock hard. Like a week or two after the rain. Get some good tools, even a chopstick can be quite useful.
Be aware that chollas (like prickly pears) have nasty spines and glochids. So handle the stem with gloves or a tool instead of your bare hands. Probably a good practice when handling any kind of mystery cactus, unless you like to live on the edge.
