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Yes, peperomia can be propagated from a cutting. For information on how to root cuttings, please visit the following links:

https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm
http://www.gardenhive.com/houseplants/peperomias/propagate/stem-cuttings/

For more information on the care of peperomia, please visit the following link:
https://www.gardeningknowhow.com/houseplants/peperomia/growing-peperomia-houseplants.htm

This is a Peperomia plant.

https://www.gardeningknowhow.com/houseplants/peperomia/growing-peperomia-houseplants.htm

If you do not have access to a good fertilizer, then repotting in the same pot, or in only a slightly bigger pot with fresh soil will help. Gently shake out the roots running under water if you can. This will help get all the old dirt out gently. Then replace with only SLIGHTLY moist soil. Try and get the crown back into the same position right above the soil level where it was before re-potting. After, water this in and top off the soil if needed.

If you have access to fertilizer, then you may not need to re-pot often.

Here is an article that will help: https://www.gardeningknowhow.com/houseplants/peperomia/growing-peperomia-houseplants.htm

Dividing these will usually kill them. There are better ways to make copies of the plant that will have less risk. Leaves, stems, and pretty much anything that you take from the plant will root to create an exact copy of the plant.

This article will help: https://www.gardeningknowhow.com/houseplants/hpgen/using-cuttings-and-leaf-cuttings-to-propagate-your-houseplants.htm

Is this planted, only, in peat moss? Or is there soil under that? They do best in a well draining organic potting mix. Make sure the container has plenty of drainage holes. They will not tolerate over watering at all.

They will not tolerate overfeeding, but peat will not have enough nutrients to sustain the plant. This article will give you more information on the care of these: https://www.gardeningknowhow.com/houseplants/pilea-plants/pilea-chinese-money-plant-info.htm

Peperomia Obtusifolia; Varieties with green leaves thrive on bright to half shady locations and should be sheltered from the sun or be exposed to shadow in summer. Great is a spot by the window facing east or west.
Use a good quality potting soil and you can even add in some cactus mix for a well draining soil mix.
Water carefully, soil should be neither too dry or too wet!