Should a Buddhist have Children? In Buddhism having a rebirth is itself a origin of all the Dukhhas. Doesn't it imply that Buddhist laymen who are married should not have children to stop this cycle of rebirth. This leads to a more generic hypothetical question as to what happens if all people in the world stop having children? 

I would like to have the answer in the Buddhist perspective.
rebirth is itself a origin of all the Dukhhas.


Not quite. Birth has a requisite condition as well. It's not the case that our birth was the ultimate origin of our suffering.


  Doesn't it imply that buddhist laymen who are married should not have children to stop this cycle of rebirth.


Not having children will not stop those beings from being reborn. There are plenty of other organisms to be reborn as on Earth and there are other realms like the Deva world as well.


  what happens if all people in the world stop having children?


The entire population of humans could all die and be reborn as insects today and it wouldn't appreciably increase their overall number: adding six billion to 10 quintillion doesn't even amount to a tenth of a percent.

So removing the human path as a rebirth target does nothing in the way of removing suffering.