I have 4 Pekin hens, no drake. At about 5 months they got all hormonal and started play mounting each other, but that's died down now (though one of my girls, sadly, still really wants to get nailed!). They started laying right on cue at 6 months (between 23 & 25 weeks from what I can tell) towards the end of this past August. They spend most of their time in their run or pool, but always have access to a coop with deep bedding for nesting. Some of them have figured it out, some have not. I think at least 2 are laying in the coop now, but someone still really likes to lay right on the ground in front of the door to their run (like, "hey mom, look what I made for you today!"). I found our first egg in their pool, 3 or 4 have been rolled under ramps. Most of the eggs laid in the coop are invisible until I've dug them out!
As your duck begins to lay, she's just learning as well and it can take some time to figure it out. On the other hand, if your pair is mating and she's gone broody at all, she may be hiding your eggs somewhere. I would definitely launch an egg hunt where they are roaming...she should be laying by now so you have some investigating to do!
You can also stick a dummy egg/nest where you want her to lay, to try and train her. But my girls seemed to know the plastic eggs I used were fake and didn't take to the coop until I removed them.
