I wouldn't be too sure to be honest since they're illegal little critters where I live. I did some research on information on breeding Hamsters for you.
Sexually mature around 30 days. May start breeding when they are between 60 and 90 days old. Size: Djungarian hamster: 30 g, Roborovski hamster: 20 – 25 g, Campbell's dwarf hamster: 27 g. Gestation period: Djungarian hamster: 21 days, Roborovski hamster: 22 days, Campbell's dwarf hamster: 18 – 20 days Not bad in weight. How large scale you breed would depend on the ferret(s). Hamsters have around average of 6-14 pups from what I read. Kind of like mice.
(Mice are 28–44 g fully grown. The gestation period for mice is about 19–21 days, and they give birth to a litter of 3–14 young (average six to eight). (I've been having 11 lately)
Nutritionally wise, It's a tight squeeze between mice and hamsters. Hamsters may have more calcium.
Most hamsters are strictly solitary. If housed together, acute and chronic stress may occur, and they may fight fiercely, sometimes fatally. Some dwarf hamster species may tolerate conspecifics. Russian hamsters form close, monogamous bonds with their mates, and if separated, they may become very depressed.
Breeding mice on the other hand, you could house them together, breed females together. I wouldn't really know if you could breed multiple hamsters in the same space though.
This is a general thing on having hamsters, but I have had multiple instances where the hamster(s) will sleep under or next to their water and die from hypothermia. I will never ever get a hamster as a pet again.