From what I hear, Pekins begin to lay around 7 months of age if they mature in relatively warm weather. Late hatches sometimes mean the ducks will wait till the next spring. But it is entirely up to the duck.
You can help your ducks by providing them with the best shelter, water and food that you can manage. About a month before they begin to lay (I used breeding behavior as a gauge for that), give them free choice oyster shell. Then get them onto layer food once they start laying. There are other strategies, by the way. I did my best to follow Storey's Guide to Raising Ducks.
Having a good drake to duck ratio (1 to 3, or 1 to 6) if you have drakes matters, too.
A reasonably calm environment helps, as stress interferes with laying.
Plenty of light, protection from extreme temperatures, those help.