If you are talking about Egyptian Fayoumi, they do mature faster than the average hen, about 4 1/2 months, or 18 to 20 weeks.
However they would have hatched in June, so they are coming to lay late summer. I've not had Fayoumi, but I've had other faster developing hybrids and find when they come to lay makes a big difference.
My summer babes are 50/50 whether they lay by September/October or wait until spring due to the shortening days. Summer soltice is mid-June, so the days are shortening after that. A pullet needs about 14 to 16 hours of daylight to trigger her pituitary gland to start laying. I'm in northern Oregon, so I don't necessarily see long enough daylight for summer babes to lay by late summer-fall.
However, I see you are in South Carolina, so your days may be a bit longer than mine are now. With that in mind, watch your pullets and see their activity. If they disappear behind a bush, meander by a bucket, you may find a hidden nest.
Good luck with the Easter Egg hunt. However, you may find they simply won't start to lay until March.
LofMc