A number of factors can influence when a duck may commence laying. Day light hours, season and breed are the most influential. Muscovies and ornamental breeds can tend to be more seasonal layers- and may not lay until the spring following their hatching - meaning they can be nearly a year old before they lay. Whereas something like a Runner or Campbell who lay year round are more likely to start when 22 weeks give or take a few weeks regardless of the season.
Generally a duck is physically mature enough to lay eggs as early as 16 weeks but an average is more around the 22- 24 weeks of age mark.
Did you have a specific breed you were wanting to know about??
With a Pekin I would say that 22- 24 would be normal so buying them early you might get some eggs in late summer. It depends a little on the strain- as pekins - being mainly a meat bird arent among the greatest layers. Having said that though - my girl laid up a storm until her current molt - laying pretty much an egg a day when she wasnt broody for a whole year.