I've had a few hens that'd go broody during times of me not collecting the eggs, but it really depends on the hen. I've gone days to weeks without collecting eggs with breeds who are known to go broody, and some went broody and some didn't. As everyone else has said, it really depends on the bird.
How old is she and has she ever gone broody before? Even though most will say hens will start brooding when they're older, I've found that not to be a factor in most cases. I've had hens go broody as early as four months old and I've had hens stop going broody in their old age, as well as 6-7 year old hens never going broody despite being a broody breed and everyone else in the flock trying it at least once.
Often, I find brooders being repeat offenders. They'll go broody within their first two years of age (some within their first year) and will be faithful every year after. If they're not allowed to hatch, they'll be determined to brood anyway and will sit until you stop them, and then go broody a month or so later.
It is getting late in the season, depending on where you live (country wise), so it might be too late to get her to go broody anyway. This isn't always the case, but for the better brooders, it is. Some of my best brooders would often go broody between June-August.
On a side note of all of this, did you get this Cochin specifically to brood? I've never had Cochins, but from what I gather, they're determined brooders, but not good mothers. If you wanted a good mother, you might want to consider a different breed like an Orpington or another breed. Otherwise, you might be raising the chicks yourself, or have a poor hatch rate. I've had Orpington brooders and they were the best. I've also had some good Marans, but my only thing on them is I couldn't fit as many eggs under them.
Also, where did you get your Cochin? Chickens from a hatchery are less likely to brood than one from a local breeder who's breeding quality. Hatcheries are typically breeding quantity and not quality, so often the breeding instinct is bred out. Plus, hens who are constantly in the nesting box is no good for a hatchery who is using incubators, so that's another reason to breed it out of them. A good breeder is typically breeding for quality and some breeders might be using their hens as brooders, so you might already have a good family line of brooders anyway.
Now I have gotten a good broody from a hatchery before and didn't get a single brooder from a breeder, so again, it depends on the bird and there's always exceptions. Most of my brooders though, came from breeders and not hatcheries.
