First of all, it sounds like you have very little understanding of how hens lay eggs, brood them, etc. I'd recommend you click on the 'learning center' link at the top of the page, or read this article for a lot more information about the process.
http://www.themodernhomestead.us/article/Broody-Hens-1.html
They don't 'learn' how to sit on the eggs and brood them - they either will, or they won't, and that varies from hen to hen, breed to breed, and going broody seems to strike like lightning even in those who tend to go broody - when the urge hits, it has little to do with how many eggs they have laid, or how many are in the nest - they will sit on nothing at all. (I've got a buff orp right now sitting on air in the nest box...)
If you want to give her the best odds to actually brood the egg, separate out the hen who laid it into her own place where she can lay her eggs in the same nest and MAYBE she will lay a few and then start to sit. If she has been with the roosters, then she will be fertile for at least a couple weeks after she was mated, so don't worry about her losing fertility if you separate her.
If you leave the nest with the eggs in it out there with them all together, you run the risk of some of the others thinking the egg looks like something good to eat and pecking it out of curiosity. If they figure out they can peck, crack and eat those yummy eggs, you'll have a real problem as egg eaters are very hard to break from the habit of pecking eggs.
IF they are going to brood the eggs (sit on them to hatch them) they will not sit on the first one - they will lay several in a clutch before they begin sitting on them full time - that is so that the chicks all hatch out at the same time.
Having said all that - going 'broody' is a hormonal thing - and she may or may not go broody at all, even if you let the eggs pile up for months. First eggs are small and usually don't hatch well anyway because there isn't enough nutrition in the egg for the developing chick until the eggs get more of a normal size.
Personally, given that she's a new layer and the time of year (they'd be hatching and growing as the weather turns cold) I'd just take the eggs and eat them.
