Going Broody?

I have 3 hens & 1 rooster and I'm wanting to start letting them hatch their eggs, instead of us eating all of them. I have 1 hen who lays in a different spot than the other two, so this morning I wrote the date on the one she laid, replaced the bedding under neath it (made it cleaner) and put it back. After I left she inspected it, as did the other hens, and kept walking away and going back to it to look. Are these behaviors of going broody? My hens are just now a year old. The spot that she's laying is secluded and away from the laying boxes, so I actually have to go INTO the coop to get the eggs that she lays. I'm unsure of what kind she is.
This is a younger picture, and she's the blurry one walking out of the picture. But she's very similar to the tan and black one (they were hatched together by a friend), but she's gray and black.