It depends on what breed you've got too. musovies, for example, don't have drake feathers, but my cayuga,s khaki campbells and white pekins do.
My babies ducks were shipped out April 30 last year and I know the female cayuga started laying in late December. There were just a few eggs, then nothing again until spring. She's a very intermittent layer, but I haven't seen any of her eggs for a couple of months.
The muscovies seem to lay only when it's warm, but again, I'm not sure how old my hen was when I got her. Her first eggs started mid summer, but she may have been from a late summer hatching. So she may have been too young to lay before that.
I had a Welsh Harlequin that was hatched out the end of March and had her first egg October 5th, so she was just over 6 months. But she has laid an egg every single day since then. I knew they were good layers, but she lays better than the chickens.
As far as telling the difference, there is a bill color difference on the Welsh that's noticable when they hatch. But I've also found that with most breeds (the exception being the Muscovies) the drakes are so quite and give more like whisper quacks while the hens are very vocal. When our three female ducklings sound off, you would think our backyard was one of the state duck conservation areas.