There are two nuts on the center cross-member that attach to a rubber isolator on the transmission. These nuts are commonly loose or missing and would be a good starting place.

Also, are you lifted/oversized tires? Sometimes the rear axle can cause a feeling of slight slack after hard braking, which is more likely after lifting or just having worn components. I've experienced this on & off over the years but it's slight (feels like a "thud") and you can tell it's the rear axle. Recent axle suspension upgrades have eliminated the issue for me.